@incollection {katz:st-local_moduli,
   AUTHOR = {Katz, N.},
    TITLE = {Serre-{T}ate local moduli},
 BOOKTITLE = {Algebraic surfaces ({O}rsay, 1976--78)},
   SERIES = {Lecture Notes in Math.},
   VOLUME = {868},
    PAGES = {138--202},
 PUBLISHER = {Springer},
  ADDRESS = {Berlin},
     YEAR = {1981},
  MRCLASS = {14K10},
 MRNUMBER = {638600 (83k:14039b)},
MRREVIEWER = {William E. Lang},
}

@book {MR638596,
     TITLE = {Surfaces alg\'ebriques},
    SERIES = {Lecture Notes in Mathematics},
    VOLUME = {868},
    EDITOR = {Giraud, Jean and Illusie, Luc and Raynaud, Michel},
      NOTE = {Seminar on Algebraic Geometry held in Orsay, 1976--78},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {1981},
     PAGES = {ii+314},
      ISBN = {3-540-10842-4},
   MRCLASS = {10D21 (14J25)},
  MRNUMBER = {638596 (82j:10052)},
}
	
@article {buzzard-calegari:gm,
    AUTHOR = {Buzzard, Kevin and Calegari, Frank},
     TITLE = {A counterexample to the {G}ouv\^ea-{M}azur conjecture},
   JOURNAL = {C. R. Math. Acad. Sci. Paris},
  FJOURNAL = {Comptes Rendus Math\'ematique. Acad\'emie des Sciences. Paris},
    VOLUME = {338},
      YEAR = {2004},
    NUMBER = {10},
     PAGES = {751--753},
      ISSN = {1631-073X},
   MRCLASS = {11F33},
  MRNUMBER = {2059481 (2005g:11070)},
MRREVIEWER = {Chandrashekhar Khare},
       DOI = {10.1016/j.crma.2004.03.016},
       URL = {http://dx.doi.org.offcampus.lib.washington.edu/10.1016/j.crma.2004.03.016},
}

@misc{ghitza:maeda,
  author={Ghitza, Alex},
  title={Maeda's conjecture for weight up to 4096},
  note = {\url{http://wstein.org/Tables/charpoly_level1/t2/ghitza.html}}
}

@book{lozano,
  author={\'Alvaro Lozano-Robledo},
  title = {Elliptic {C}urves, {M}odular {F}orms and their {L}-functions},
 PUBLISHER = {American Mathematical Society},
  year={2011}
}  

@article{mpfr,
  author = {Paul Zimmerman and others},
  title = {The {MPFR} {L}ibrary},
  note = {\url{http://www.mpfr.org/}}
}

@article{mpir,
  author = {Bill Hart and others},
  title = {MPIR: Multiprecision Integers and Rationals},
  note = {\url{http://www.mpir.org/}}
}

@article{pynac,
  author = {Burcin Erocal and William Stein},
  title = {Pynac -- symbolic computation with Python objects},
  note = {\url{http://pynac.sagemath.org/}}
}

@article{ beezer:siam,
  title = {SIAM {R}eview of {S}age},
  author = {Beezer, R.},
  note = {\url{http://buzzard.ups.edu/bookreview/sage-beezer-review.pdf}},
  volume = {51},
  number = {4},
  pages = {785--807},
  year = {2009}
}

@Article{	  gfan,
  title		= {GFan: software for computing {G}r\"obner fans and tropical varieties},
  author	= {A. Jensen},
  note = {\url{http://www.math.tu-berlin.de/~jensen/software/gfan/gfan.html}}
}

@article{ginac,
  title = {GiNaC: is not a {CAS}},
  note = {\url{http://www.ginac.de/}}
}

@Article{	  flint,
  author	= {Bill Hart and David Harvey},
  title		= {FLINT: Fast Library for Number Theory},
  note          = {\url{http://www.flintlib.org/}}
}

@Article{	  cython,
  author	= {Stefan Behnel and Robert Bradshaw and Dag Seljebotn},
  title		= {Cython},
  note = {\url{http://www.cython.org/}}
}

@article {threefields,
    AUTHOR = {Mu{\~n}oz, Vicente and Persson, Ulf},
     TITLE = {Interviews with three {F}ields medalists},
   JOURNAL = {Notices Amer. Math. Soc.},
  FJOURNAL = {Notices of the American Mathematical Society},
    VOLUME = {54},
      YEAR = {2007},
    NUMBER = {3},
     PAGES = {405--410},
      ISSN = {0002-9920},
     CODEN = {AMNOAN},
   MRCLASS = {01A70},
  MRNUMBER = {MR2292145},
}


@article {howard:kolyvagin,
    AUTHOR = {Howard, Benjamin},
     TITLE = {The {H}eegner point {K}olyvagin system},
   JOURNAL = {Compos. Math.},
  FJOURNAL = {Compositio Mathematica},
    VOLUME = {140},
      YEAR = {2004},
    NUMBER = {6},
     PAGES = {1439--1472},
      ISSN = {0010-437X},
   MRCLASS = {11G05 (11R23)},
  MRNUMBER = {MR2098397 (2006a:11070)},
MRREVIEWER = {Henri Darmon},
}
	


@incollection {gross:heegnerX0N,
    AUTHOR = {Gross, Benedict H.},
     TITLE = {Heegner points on {$X_0(N)$}},
 BOOKTITLE = {Modular forms ({D}urham, 1983)},
    SERIES = {Ellis Horwood Ser. Math. Appl.: Statist. Oper. Res.},
     PAGES = {87--105},
 PUBLISHER = {Horwood},
   ADDRESS = {Chichester},
      YEAR = {1984},
   MRCLASS = {11G05 (11G16 11G40)},
  MRNUMBER = {MR803364 (87f:11036b)},
MRREVIEWER = {Loren D. Olson},
}

@book {MR803359,
     TITLE = {Modular forms},
    SERIES = {Ellis Horwood Series in Mathematics and its Applications:
              Statistics and Operational Research},
    EDITOR = {Rankin, Robert A.},
      NOTE = {Papers from the symposium held at the University of Durham,
              Durham, June 30--July 10, 1983},
 PUBLISHER = {Ellis Horwood Ltd.},
   ADDRESS = {Chichester},
      YEAR = {1984},
     PAGES = {272},
      ISBN = {0-85312-669-0},
   MRCLASS = {11-06},
  MRNUMBER = {MR803359 (86f:11003)},
}
		

@article{stein:modabvarnotes,
   author={William Stein},
   title={Computational Number Theory Course Notes},
   date={2009},
   note={\url{http://wiki.wstein.org/09/583e}}
}


@book {MR2023284,
     TITLE = {Geometric aspects of {D}work theory. {V}ol. {I}, {II}},
    EDITOR = {Adolphson, Alan and Baldassarri, Francesco and Berthelot,
              Pierre and Katz, Nicholas and Loeser, Fran{\c{c}}ois},
      NOTE = {Lectures from the Dwork trimester dedicated to Bernard Dwork
              held at the University of Padova, Padova, May--July 2001},
 PUBLISHER = {Walter de Gruyter GmbH \& Co. KG, Berlin},
      YEAR = {2004},
     PAGES = {Vol. I: xiv+554 pp.; Vol. II: pp. i--vi and 555--1129},
      ISBN = {3-11-017478-2},
   MRCLASS = {00B30 (11-06 12-06 14-06)},
  MRNUMBER = {MR2023284 (2005f:00015)},
}


@incollection {coleman-stein:padicapprox,
    AUTHOR = {Coleman, Robert F. and Stein, William A.},
     TITLE = {Approximation of eigenforms of infinite slope by eigenforms of
              finite slope},
 BOOKTITLE = {Geometric aspects of {D}work theory. {V}ol. {I}, {II}},
     PAGES = {437--449},
 PUBLISHER = {Walter de Gruyter GmbH \& Co. KG, Berlin},
      YEAR = {2004},
   MRCLASS = {11F33 (11F11)},
  MRNUMBER = {MR2023296 (2005h:11092)},
MRREVIEWER = {Mark Kisin},
}


@article{trilliontri,
   title={A Trillion Triangles},
   date={September 22, 2009},
   note={\url{http://aimath.org/news/congruentnumbers/}}
}

@article {mazur:meaning,
    AUTHOR = {Mazur, Barry},
     TITLE = {Finding meaning in error terms},
   JOURNAL = {Bull. Amer. Math. Soc. (N.S.)},
  FJOURNAL = {American Mathematical Society. Bulletin. New Series},
    VOLUME = {45},
      YEAR = {2008},
    NUMBER = {2},
     PAGES = {185--228},
      ISSN = {0273-0979},
     CODEN = {BAMOAD},
   MRCLASS = {11G05 (11-02 11F03 11F80 11G40 14G10)},
  MRNUMBER = {MR2383303 (2009c:11083)},
MRREVIEWER = {David Y. Jao},
}


@article{joyner-stein:notices,
  author={Stein, William and Joyner, David},
  title={Open source mathematical software},
  year={2007},
   JOURNAL = {Notices Amer. Math. Soc.},
  FJOURNAL = {Notices of the American Mathematical Society},
note={\url{http://www.ams.org/notices/200710/tx071001279p.pdf}}
}  

@article{cornut:mazur,
  author={Cornut, Christophe},
  title={Mazur's conjecture on higher Heegner points}
}

@article{jetchev-kane:equi,
  author = {Jetchev, Dimitar and Kane, Ben},
  title = {Equidistribution of {H}eegner {P}oints and {T}ernary {Q}uadratic {F}orms},
  year = 2009,
}

@article{stein:kolyconj2,
  author = {Stein, William},
  title = {Heegner Points on Rank Two Elliptic Curves},
  year = {2009},
  note = {\url{http://wstein.org/papers/kolyconj2/}}
}

@article{stein:ggz,
  author = {Stein, William},
  title = {Toward a {G}eneralization of the {G}ross-{Z}agier {C}onjecture},
  year = {2009},
  note = {\url{http://wstein.org/papers/stein-ggz/}, submitted}
}


@book {cohen:gtm240,
    AUTHOR = {Cohen, Henri},
     TITLE = {Number theory. {V}ol. {II}. {A}nalytic and modern tools},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {240},
 PUBLISHER = {Springer},
   ADDRESS = {New York},
      YEAR = {2007},
     PAGES = {xxiv+596},
      ISBN = {978-0-387-49893-5},
   MRCLASS = {11-01 (11D61 11F80 11J86 11Mxx)},
  MRNUMBER = {MR2312338 (2008e:11002)},
MRREVIEWER = {R. C. Baker},
}
		


@book {cohen:gtm239,
    AUTHOR = {Cohen, Henri},
     TITLE = {Number theory. {V}ol. {I}. {T}ools and {D}iophantine
              equations},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {239},
 PUBLISHER = {Springer},
   ADDRESS = {New York},
      YEAR = {2007},
     PAGES = {xxiv+650},
      ISBN = {978-0-387-49922-2},
   MRCLASS = {11-01 (11Dxx 11Rxx 11Sxx)},
  MRNUMBER = {MR2312337 (2008e:11001)},
MRREVIEWER = {R. C. Baker},
}

@article{khare-wintenberger:serre1,
   author = {Khare, C. and Wintenberger, J.-P.},
   title = {Serre's Modularity Conjecture (I)},
   journal = {Preprint},
   year = {2008}
}


@book {diamond-shurman,
    AUTHOR = {Diamond, Fred and Shurman, Jerry},
     TITLE = {A first course in modular forms},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {228},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {New York},
      YEAR = {2005},
     PAGES = {xvi+436},
      ISBN = {0-387-23229-X},
   MRCLASS = {11Fxx},
MRREVIEWER = {Henri Darmon},
}

@article{calegari-stein:eisenstein,
AUTHOR = {Calegari, Frank and Stein, William},
TITLE = {A non-{G}orenstein {E}isenstein descent},
YEAR = {2008},
NOTE = {In Preparation}
}

@incollection {MR2282913,
    AUTHOR = {Edixhoven, Bas},
     TITLE = {On the computation of the coefficients of a modular form},
 BOOKTITLE = {Algorithmic number theory},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {4076},
     PAGES = {30--39},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {2006},
   MRCLASS = {11F80 (11F30 11Y35)},
  MRNUMBER = {MR2282913 (2007k:11085)},
MRREVIEWER = {Jeremy A. Rouse},
}

@proceedings {MR2281142,
     TITLE = {Algorithmic number theory},
    SERIES = {Lecture Notes in Computer Science},
    VOLUME = {4076},
 BOOKTITLE = {Proceedings of the 7th International Symposium (ANTS-VII) held
              at the Technische Universit\"at Berlin, Berlin, July 23--28,
              2006},
    EDITOR = {Hess, Florian and Pauli, Sebastian and Pohst, Michael},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {2006},
     PAGES = {x+598},
      ISBN = {978-3-540-36075-9; 3-540-36075-1},
   MRCLASS = {11-06 (11Y16)},
  MRNUMBER = {MR2281142 (2007h:11001)},
}
		

@article{harvey:padicheights,
  author = {Harvey, David},
  title = {Efficient computation of p-adic heights},
  year = {2007},
  note = {\url{http://arxiv.org/abs/0708.3404}}
}


@book {cohen:nt2,
    AUTHOR = {Cohen, Henri},
     TITLE = {Number theory. {V}ol. {II}. {A}nalytic and modern tools},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {240},
 PUBLISHER = {Springer},
   ADDRESS = {New York},
      YEAR = {2007},
     PAGES = {xxiv+596},
      ISBN = {978-0-387-49893-5},
   MRCLASS = {11-01 (11D04 11D09)},
  MRNUMBER = {MR2312338}
}
	

@book {stein:modform,
    AUTHOR = {Stein, William},
     TITLE = {Modular forms, a computational approach},
    SERIES = {Graduate Studies in Mathematics},
    VOLUME = {79},
      NOTE = {With an appendix by Paul E. Gunnells},
 PUBLISHER = {American Mathematical Society},
   ADDRESS = {Providence, RI},
      YEAR = {2007},
     PAGES = {xvi+268},
      ISBN = {978-0-8218-3960-7; 0-8218-3960-8},
   MRCLASS = {11-01 (11F11 11F67 11Y16)},
  MRNUMBER = {MR2289048},
}
	

@book{stein:bsd,
  author = {Stein, W.},
  title = {The {B}irch and {S}winnerton-{D}yer {C}onjecture, a {C}omputational {A}pproach},
   year = {2007},
  note = {http://wstein.org/edu/2007/spring/bsd/}
}

@article{msri06modform,
  author = {Stein, W.},
  title = {Workshop: Computing with Modular Forms},
  year = {July 31 -- August 11, 2006},
  note = {\url{http://wstein.org/msri06}}
}

@article{mazur:nature,
   author = {Mazur, B.},
   title = {Controlling our errors},
   journal = {Nature},
   volume = {443},
   year = {7 September 
   2006}
}

@article{gordon:db,
   author = {Gordon, D.},
   title = {Databases of coverings and cyclic difference sets},
   note = {\url{http://www.ccrwest.org/gordon/dan.html}}
}

@article{openmath,
   author = {OpenMath},
   title = {An extensible standard for representing the semantics of mathematical objects},
   note = {\url{http://www.openmath.org/}}
}


@book{gathengerhard,
    author = {Gathen, Joachim von zur and Gerhard, Jrgen},
  title = {Modern {C}omputer {A}lgebra},
 PUBLISHER = {Cambridge University Press},
      YEAR = {2003},
     PAGES = {xiv+786},
      ISBN = {0521826462 }
}

@article{axiom,
  title = {A general purpose system for doing mathematics by computer},
  author = {Axiom},
  note = {\url{http://wiki.axiom-developer.org/}}
}


@article{scipy06,
  title = {Conference on {S}cientific {C}omputation using {P}ython},
  author = {SCIPY},
  year = {2006},
    note = {\url{http://www.scipy.org/SciPy2006/Schedule}}
}

@article{stein:studentprojects,
  title = {{W}illiam {S}tein's {S}tudent {P}rojects},
  author = {Stein, W.},
  note = {\url{http://wstein.org/projects}},
  year = {2006},
}


@article{lie,
  title = {{LiE}: {A} {C}omputer algebra package for {L}ie group computations},
  author = {van Leeuwen, M.},
  note = {\url{http://www-math.univ-poitiers.fr/~maavl/LiE/}}
}

@article{gap,
  title = {GAP: Groups, Algorithms and Programming},
  note = {\url{http://www.gap-system.org/}},
  author = {Gap Group}
}

@article{singular,
  author = {Singular},
  title = {A Computer Algebra System for polynomial computations},
  note = {\url{http://www.singular.uni-kl.de/}}
}

@article{pari,
  author = {PARI},
  title = {A computer algebra system designed for fast computations in number theory},
  note = {\url{http://pari.math.u-bordeaux.fr/}}
}

@article{maxima,
  title = {MAXIMA: A {C}omputer {A}lgebra {S}ystem},
  note = {\url{http://maxima.sourceforge.net/}},
}

@Misc{M2,
          author = {Grayson, Daniel R. and Stillman, Michael E.},
          title = {Macaulay2, a software system for research 
                   in algebraic geometry},
          howpublished = {Available at 
              \href{http://www.math.uiuc.edu/Macaulay2/}%
                   {http://www.math.uiuc.edu/Macaulay2/}}
        }

@article{macaulay2,
  author = {Grayson, D. and Stillman, M.},
  title = {{Macaulay2: a software system devoted to supporting research in algebraic geometry and commutative algebra}},
  note = {\url{http://www.math.uiuc.edu/Macaulay2/}}
}


@article{jetchev-lauter-stein,
   author = {Jetchev, D. and Lauter, K. and Stein, W.},
    title = {Explicit Heegner Points: {K}olyvagin's Conjecture and Nontrivial Elements in the {S}hafarevich-{T}ate Group},
    year = {2007},
    note = {published, \url{http://wstein.org/papers/kolyconj/}}
}

@article{stein-wuthrich,
   AUTHOR = {Stein, W. and Wuthrich, C.},
   TITLE = {Computations {A}bout {T}ate-{S}hafarevich {G}roups {U}sing {I}wasawa {T}heory},
   JOURNAL = {In preparation},
   YEAR = {2010},
   note = {\url{http://wstein.org/papers/shark/}}
}

@incollection {pernet:charpoly,
    AUTHOR = {Dumas, Jean-Guillaume and Pernet, Cl{\'e}ment and Wan,
              Zhendong},
     TITLE = {Efficient computation of the characteristic polynomial},
 BOOKTITLE = {ISSAC'05},
     PAGES = {140--147 (electronic)},
 PUBLISHER = {ACM},
   ADDRESS = {New York},
      YEAR = {2005},
   MRCLASS = {68W30 (15A18)},
  MRNUMBER = {MR2280540},
}

@article {pacetti-villegas,
    AUTHOR = {Pacetti, Ariel and Rodriguez Villegas, Fernando},
     TITLE = {Computing weight 2 modular forms of level {$p\sp 2$}},
      NOTE = {With an appendix by B.\ Gross},
   JOURNAL = {Math. Comp.},
  FJOURNAL = {Mathematics of Computation},
    VOLUME = {74},
      YEAR = {2005},
    NUMBER = {251},
     PAGES = {1545--1557 (electronic)},
      ISSN = {0025-5718},
     CODEN = {MCMPAF},
   MRCLASS = {11F11 (11E20 11F25)},
  MRNUMBER = {MR2137017 (2006a:11053)},
MRREVIEWER = {B. Ramakrishnan},
}
		
@article{gabor-koopa-stein,
   author = {Koo, K. and Stein, W. and Weise, G.},
   title = {On the generation of the coefficient field of a newform by a single Hecke eigenvalue},
   journal = {Preprint},
   year = {2007}
}

@article {elkies:supersingular,
    AUTHOR = {Elkies, Noam D.},
     TITLE = {The existence of infinitely many supersingular primes for
              every elliptic curve over {${\bf Q}$}},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {89},
      YEAR = {1987},
    NUMBER = {3},
     PAGES = {561--567},
      ISSN = {0020-9910},
     CODEN = {INVMBH},
   MRCLASS = {11G05 (14G25)},
  MRNUMBER = {MR903384 (88i:11034)},
MRREVIEWER = {David Grant},
}
	
@article {siksekcremona,
    AUTHOR = {Siksek, Samir and Cremona, John E.},
     TITLE = {On the {D}iophantine equation {$x\sp 2+7=y\sp m$}},
   JOURNAL = {Acta Arith.},
  FJOURNAL = {Acta Arithmetica},
    VOLUME = {109},
      YEAR = {2003},
    NUMBER = {2},
     PAGES = {143--149},
      ISSN = {0065-1036},
     CODEN = {AARIA9},
   MRCLASS = {11G30 (11D41)},
  MRNUMBER = {1980642 (2004c:11109)},
MRREVIEWER = {Dimitrios Poulakis},
}

@article { chen:dio,
    AUTHOR = {Chen, Imin},
     TITLE = {A {D}iophantine equation associated to {$X\sb 0(5)$}},
   JOURNAL = {LMS J. Comput. Math.},
  FJOURNAL = {LMS Journal of Computation and Mathematics},
    VOLUME = {8},
      YEAR = {2005},
     PAGES = {116--121 (electronic)},
      ISSN = {1461-1570},
   MRCLASS = {11G05 (11D41 11G18 14G05)},
  MRNUMBER = {2153792 (2006b:11052)},
MRREVIEWER = {Mihran Papikian},
}

@article {merel:diophantine,
    AUTHOR = {Merel, L.},
     TITLE = {Arithmetic of elliptic curves and {D}iophantine equations},
      NOTE = {Les XX\`emes Journ\'ees Arithm\'etiques (Limoges, 1997)},
   JOURNAL = {J. Th\'eor. Nombres Bordeaux},
  FJOURNAL = {Journal de Th\'eorie des Nombres de Bordeaux},
    VOLUME = {11},
      YEAR = {1999},
    NUMBER = {1},
     PAGES = {173--200},
      ISSN = {1246-7405},
   MRCLASS = {11G05 (11D41 11G18)},
  MRNUMBER = {1730439 (2000j:11084)},
MRREVIEWER = {Andrea Mori},
}


@article {darmon:eps,
    AUTHOR = {Darmon, H.},
     TITLE = {Faltings plus epsilon, {W}iles plus epsilon, and the
              generalized {F}ermat equation},
   JOURNAL = {C. R. Math. Rep. Acad. Sci. Canada},
  FJOURNAL = {La Soci\'et\'e Royale du Canada. L'Acad\'emie des Sciences.
              Comptes Rendus Math\'ematiques (Mathematical Reports)},
    VOLUME = {19},
      YEAR = {1997},
    NUMBER = {1},
     PAGES = {3--14},
      ISSN = {0706-1994},
   MRCLASS = {11D41 (11G18 14G25)},
  MRNUMBER = {1479291 (98h:11034a)},
MRREVIEWER = {Andrew Bremner},
}


@manual{sage,
  Key          = {Sage},
  Author       = {W.\thinspace{}A. Stein and others},
  Organization = {The Sage Development Team},
  Title        = {{S}age {M}athematics {S}oftware ({V}ersion 4.3.1)},
  note         = {{\tt http://www.sagemath.org}},
  Year         = {2010},
}

@article {cps:bound,
    AUTHOR = {Cremona, J. E. and Prickett, M. and Siksek, Samir},
     TITLE = {Height difference bounds for elliptic curves over number
              fields},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {116},
      YEAR = {2006},
    NUMBER = {1},
     PAGES = {42--68},
      ISSN = {0022-314X},
     CODEN = {JNUTA9},
   MRCLASS = {11G50 (11G05)},
  MRNUMBER = {MR2197860 (2006k:11121)},
MRREVIEWER = {Clayton Petsche},
}

@article{simuw,
   AUTHOR = {SIMUW},
   title = {Summer {I}nstitute of {M}athematics at {U}niversity
   of {W}ashington},
   note = {\url{http://wstein.org/simuw/}}
}

@article{stein:vismw,
  author={Stein, W.},
  title ={Visibility of Mordell-Weil Groups},
  pages={20},
  note = {to appear in Documenta Mathematica}
}  
  

@article {bmsw:bulletins,
    AUTHOR = {Bektemirov, Baur and Mazur, Barry and Stein, William and
              Watkins, Mark},
     TITLE = {Average ranks of elliptic curves: tension between data and
              conjecture},
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@article {coul,
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@Unpublished{vdk,
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  title = 	 {{Programs to compute Hecke eigenforms}},
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}


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MRREVIEWER = {Kazuyuki Hatada},
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@incollection {mmc2,
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}

@article {staffeldt,
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  MRNUMBER = {552526 (80m:22014)},
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@misc{harder-arbeit,
  author = {Harder, G.},
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  date = {2003}
}


@article {gunnells:experimental,
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     TITLE = {Computing {H}ecke eigenvalues below the cohomological
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   JOURNAL = {Experiment. Math.},
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@book{stein:book,
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}

@article{edixhoven:kedlaya,
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    TITLE = {Point counting after {K}edlaya, {E}{I}{D}{M}{A}-{S}tieltjes Graduate course, {L}eiden, {S}eptember 22-26,2003,\hfill\\
{\tt http://www.math.leidenuniv.nl/~edix/oww/mathofcrypt/carls\_edixhoven/kedlaya.pdf}
}}

@incollection{kedlaya:mw2,
    AUTHOR = {Kedlaya, K.},
     TITLE = {Computing zeta functions via {$p$}-adic cohomology},
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      YEAR = {2004},
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@article {mazur-stein-tate:padic,
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  MRNUMBER = {MR2290599 (2007i:11089)},
MRREVIEWER = {Thomas A. Weston},
}
		

@article{hoeij:nf,
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   year = {2006}
}

@article {dokchitser:lfun,
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@incollection {mazur-rubin:pairings_arith,
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     TITLE = {Pairings in the arithmetic of elliptic curves},
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}

@book {MR2058638,
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 PUBLISHER = {Birkh\"auser Verlag},
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     PAGES = {viii+289},
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  MRNUMBER = {MR2058638 (2004k:11004)},
}


@article{calegari-emerton:odd,
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   year = {2005}
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@article {MR1413578,
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              1993)},
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@book {MR1659828,
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 PUBLISHER = {American Mathematical Society},
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      YEAR = {1999},
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MRREVIEWER = {Philippe G. Michel},
}

@article {oMR1930670,
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@misc{cprw,
  author = {Conrey, J.~B. and Pokharel, A. and Rubinstein, M.~O. and 
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  title = {Secondary terms in the number of vanishings of quadratic twists of  elliptic curve L-functions\\
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  year = {2005}
}

@book{katz-sarnak,
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   title = {Random Matrices, Frobenius Eigenvalues, and Monodromy (Colloquium Publications (Amer Mathematical Soc))}, 
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}


@article {MR1317641,
    AUTHOR = {Coleman, Robert F. and Gouv{\^e}a, Fernando Q. and Jochnowitz,
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     TITLE = {{$E\sb 2$}, {$\Theta$}, and overconvergence},
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    NUMBER = {1},
     PAGES = {23--41 (electronic)},
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@article {MR1977007,
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      YEAR = {2003},
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  MRNUMBER = {MR1977007 (2004c:11097)},
MRREVIEWER = {Vinayak Vatsal},
}


@article {MR1740990,
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    NUMBER = {3},
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  MRNUMBER = {MR1740990 (2001a:11108)},
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@article {MR2122612,
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     CODEN = {JNUTA9},
   MRCLASS = {11G10 (11F33 11G18)},
  MRNUMBER = {MR2122612},
MRREVIEWER = {Mihran Papikian},
}

@incollection {MR2088713,
    AUTHOR = {Flach, Matthias},
     TITLE = {The equivariant {T}amagawa number conjecture: a survey},
 BOOKTITLE = {Stark's conjectures: recent work and new directions},
    SERIES = {Contemp. Math.},
    VOLUME = {358},
     PAGES = {79--125},
      NOTE = {With an appendix by C.\ Greither},
 PUBLISHER = {Amer. Math. Soc.},
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      YEAR = {2004},
   MRCLASS = {11G40 (11G18 11R23 11R33)},
  MRNUMBER = {MR2088713},
MRREVIEWER = {Nigel Byott},
}


@book {MR2090725,
     TITLE = {Stark's conjectures: recent work and new directions},
    SERIES = {Contemporary Mathematics},
    VOLUME = {358},
    EDITOR = {Burns, David and Sands, Jonathan},
      NOTE = {Papers from the International Conference on Stark's
              Conjectures and Related Topics held at Johns Hopkins
              University, Baltimore, MD, August 5--9, 2002},
 PUBLISHER = {American Mathematical Society},
   ADDRESS = {Providence, RI},
      YEAR = {2004},
     PAGES = {x+221},
      ISBN = {0-8218-3480-0},
   MRCLASS = {11-06 (11R42)},
  MRNUMBER = {MR2090725 (2005d:11004)},
}


@article {MR2135139,
    AUTHOR = {Vatsal, V.},
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}

@article{bluher:formal,
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and {E}lliptic {C}urves,\\
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}



@incollection {MR1263527,
    AUTHOR = {Nekov{\'a}{\v{r}}, Jan},
     TITLE = {On {$p$}-adic height pairings},
 BOOKTITLE = {S\'eminaire de Th\'eorie des Nombres, Paris, 1990--91},
    SERIES = {Progr. Math.},
    VOLUME = {108},
     PAGES = {127--202},
 PUBLISHER = {Birkh\"auser Boston},
   ADDRESS = {Boston, MA},
      YEAR = {1993},
   MRCLASS = {11G09 (11F85 14F30)},
  MRNUMBER = {MR1263527 (95j:11050)},
MRREVIEWER = {Abdellah Mokrane},
}


 
@book {MR1263519,
     TITLE = {S\'eminaire de {T}h\'eorie des {N}ombres, {P}aris, 1990--91},
    SERIES = {Progress in Mathematics},
    VOLUME = {108},
    EDITOR = {David, Sinnou},
      NOTE = {Papers from the seminar held in Paris, 1990--1991},
 PUBLISHER = {Birkh\"auser Boston Inc.},
   ADDRESS = {Boston, MA},
      YEAR = {1993},
     PAGES = {vi+282},
      ISBN = {0-8176-3684-6},
   MRCLASS = {11-06},
  MRNUMBER = {MR1263519 (94i:11005)},
}

@incollection {MR1042777,
    AUTHOR = {Zarhin, Yuri G.},
     TITLE = {{$p$}-adic heights on abelian varieties},
 BOOKTITLE = {S\'eminaire de Th\'eorie des Nombres, Paris 1987--88},
    SERIES = {Progr. Math.},
    VOLUME = {81},
     PAGES = {317--341},
 PUBLISHER = {Birkh\"auser Boston},
   ADDRESS = {Boston, MA},
      YEAR = {1990},
   MRCLASS = {11G10 (14K15)},
  MRNUMBER = {MR1042777 (91f:11043)},
MRREVIEWER = {Michel Gros},
}

 
@book {MR1042761,
     TITLE = {S\'eminaire de {T}h\'eorie des {N}ombres, {P}aris 1987--88},
    SERIES = {Progress in Mathematics},
    VOLUME = {81},
    EDITOR = {Goldstein, Catherine},
      NOTE = {Papers from the seminar held in Paris, 1987--88},
 PUBLISHER = {Birkh\"auser Boston Inc.},
   ADDRESS = {Boston, MA},
      YEAR = {1990},
     PAGES = {viii+350},
      ISBN = {0-8176-3458-4},
   MRCLASS = {11-06},
  MRNUMBER = {MR1042761 (90j:11004)},
}


@incollection {MR1299736,
    AUTHOR = {Plater, Andrew},
     TITLE = {Supersingular {$p$}-adic height pairings on elliptic curves},
 BOOKTITLE = {Arithmetic geometry (Tempe, AZ, 1993)},
    SERIES = {Contemp. Math.},
    VOLUME = {174},
     PAGES = {95--105},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, RI},
      YEAR = {1994},
   MRCLASS = {11G07 (11G05)},
  MRNUMBER = {MR1299736 (95h:11056)},
MRREVIEWER = {Jan Nekov{\'a}{\v{r}}},
}

 
@book {MR1299731,
     TITLE = {Arithmetic geometry},
    SERIES = {Contemporary Mathematics},
    VOLUME = {174},
    EDITOR = {Childress, Nancy and Jones, John W.},
      NOTE = {Papers from the Conference on Arithmetic Geometry with an
              Emphasis on Iwasawa Theory held at Arizona State University,
              Tempe, Arizona, March 15--18, 1993},
 PUBLISHER = {American Mathematical Society},
   ADDRESS = {Providence, RI},
      YEAR = {1994},
     PAGES = {x+220},
      ISBN = {0-8218-5174-8},
   MRCLASS = {11-06 (11Fxx 11Gxx)},
  MRNUMBER = {MR1299731 (95d:11002)},
}


@article {MR1091621,
    AUTHOR = {Coleman, Robert F.},
     TITLE = {The universal vectorial bi-extension and {$p$}-adic heights},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {103},
      YEAR = {1991},
    NUMBER = {3},
     PAGES = {631--650},
      ISSN = {0020-9910},
     CODEN = {INVMBH},
   MRCLASS = {14F30 (14K15)},
  MRNUMBER = {MR1091621 (92k:14021)},
MRREVIEWER = {Gerd Faltings},
}


@article {MR2021039,
    AUTHOR = {Iovita, Adrian and Werner, Annette},
     TITLE = {{$p$}-adic height pairings on abelian varieties with
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   JOURNAL = {J. Reine Angew. Math.},
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    VOLUME = {564},
      YEAR = {2003},
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      ISSN = {0075-4102},
     CODEN = {JRMAA8},
   MRCLASS = {11G50 (11G10 14F40 14K15)},
  MRNUMBER = {MR2021039 (2004j:11066)},
MRREVIEWER = {Alessandra Bertapelle},
}

@incollection {MR2076563,
    AUTHOR = {Besser, Amnon},
     TITLE = {The {$p$}-adic height pairings of {C}oleman-{G}ross and of
              {N}ekov\'a\v r},
 BOOKTITLE = {Number theory},
    SERIES = {CRM Proc. Lecture Notes},
    VOLUME = {36},
     PAGES = {13--25},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, RI},
      YEAR = {2004},
   MRCLASS = {11G50 (11G25 11G30)},
  MRNUMBER = {MR2076563 (2005f:11130)},
MRREVIEWER = {Mark Kisin},
}

 
@book {MR2070918,
     TITLE = {Number theory},
    SERIES = {CRM Proceedings \& Lecture Notes},
    VOLUME = {36},
    EDITOR = {Kisilevsky, Hershy and Goren, Eyal Z.},
      NOTE = {Papers from the 7th Conference of the Canadian Number Theory
              Association held at the University of Montreal, Montreal, QC,
              May 19--25, 2002},
 PUBLISHER = {American Mathematical Society},
   ADDRESS = {Providence, RI},
      YEAR = {2004},
     PAGES = {xiv+303},
      ISBN = {0-8218-3331-6},
   MRCLASS = {11-06},
  MRNUMBER = {MR2070918 (2005b:11004)},
}

@article {perrin-riou:expmath,
    AUTHOR = {Perrin-Riou, Bernadette},
     TITLE = {Arithm\'etique des courbes elliptiques \`a r\'eduction
              supersinguli\`ere en {$p$}},
   JOURNAL = {Experiment. Math.},
  FJOURNAL = {Experimental Mathematics},
    VOLUME = {12},
      YEAR = {2003},
    NUMBER = {2},
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      ISSN = {1058-6458},
   MRCLASS = {11G40 (11G05 11R23)},
  MRNUMBER = {MR2016704 (2005h:11138)},
}

@article {mazur-tate:refined,
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     TITLE = {Refined conjectures of the ``{B}irch and {S}winnerton-{D}yer
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   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {54},
      YEAR = {1987},
    NUMBER = {2},
     PAGES = {711--750},
      ISSN = {0012-7094},
     CODEN = {DUMJAO},
   MRCLASS = {11G40 (11G05 14G25 14K15)},
  MRNUMBER = {MR899413 (88k:11039)},
MRREVIEWER = {Karl Rubin},
}

@article {wuthrich:heightfamily,
    AUTHOR = {Wuthrich, Christian},
     TITLE = {On {$p$}-adic heights in families of elliptic curves},
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    VOLUME = {70},
      YEAR = {2004},
    NUMBER = {1},
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      ISSN = {0024-6107},
     CODEN = {JLMSAK},
   MRCLASS = {11G50 (11G05)},
  MRNUMBER = {MR2064750},
}

@article {schneider:height1,
    AUTHOR = {Schneider, Peter},
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   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {69},
      YEAR = {1982},
    NUMBER = {3},
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      ISSN = {0020-9910},
     CODEN = {INVMBH},
   MRCLASS = {14K15 (12A70 14G25)},
  MRNUMBER = {MR679765 (84e:14034)},
MRREVIEWER = {Reinhard B{\"o}lling},
}

@article {schneider:height2,
    AUTHOR = {Schneider, Peter},
     TITLE = {{$p$}-adic height pairings. {II}},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {79},
      YEAR = {1985},
    NUMBER = {2},
     PAGES = {329--374},
      ISSN = {0020-9910},
     CODEN = {INVMBH},
   MRCLASS = {11G10 (11G40 11R23 14G25)},
  MRNUMBER = {MR778132 (86j:11063)},
MRREVIEWER = {Reinhard B{\"o}lling},
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@incollection {mazur-tate:canonical,
    AUTHOR = {Mazur, B. and Tate, J.},
     TITLE = {Canonical height pairings via biextensions},
 BOOKTITLE = {Arithmetic and geometry, Vol. I},
    SERIES = {Progr. Math.},
    VOLUME = {35},
     PAGES = {195--237},
 PUBLISHER = {Birkh\"auser Boston},
   ADDRESS = {Boston, MA},
      YEAR = {1983},
   MRCLASS = {14K15 (11G10 11G35 14G25)},
  MRNUMBER = {MR717595 (85j:14081)},
MRREVIEWER = {Yu. G. Zarkhin},
}
@book {MR717602,
     TITLE = {Arithmetic and geometry. {V}ol. {II}},
    SERIES = {Progress in Mathematics},
    VOLUME = {36},
    EDITOR = {Artin, Michael and Tate, John},
      NOTE = {Geometry,
              Papers dedicated to I. R. Shafarevich on the occasion of his
              sixtieth birthday},
 PUBLISHER = {Birkh\"auser Boston},
   ADDRESS = {Mass.},
      YEAR = {1983},
     PAGES = {vi+481},
      ISBN = {3-7643-3133-X},
   MRCLASS = {14-06},
  MRNUMBER = {MR717602 (84j:14005b)},
}
@book {MR717586,
     TITLE = {Arithmetic and geometry. {V}ol. {I}},
    SERIES = {Progress in Mathematics},
    VOLUME = {35},
    EDITOR = {Artin, Michael and Tate, John},
      NOTE = {Arithmetic,
              Papers dedicated to I. R. Shafarevich on the occasion of his
              sixtieth birthday},
 PUBLISHER = {Birkh\"auser Boston},
   ADDRESS = {Mass.},
      YEAR = {1983},
     PAGES = {vi+359},
      ISBN = {3-7643-3132-1},
   MRCLASS = {14-06 (10-06 12-06)},
  MRNUMBER = {MR717586 (84j:14005a)},
}


@incollection {katz:padicprop,
    AUTHOR = {Katz, Nicholas M.},
     TITLE = {{$p$}-adic properties of modular schemes and modular forms},
 BOOKTITLE = {Modular functions of one variable, III (Proc. Internat. Summer
              School, Univ. Antwerp, Antwerp, 1972)},
     PAGES = {69--190. Lecture Notes in Mathematics, Vol. 350},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {1973},
   MRCLASS = {10D15 (14D20)},
  MRNUMBER = {MR0447119 (56 \#5434)},
MRREVIEWER = {V. V. Sokurov},
}

@book {MR0323724,
     TITLE = {Modular functions of one variable. {III}},
 BOOKTITLE = {Proceedings of the International Summer School, University of
              Antwerp, RUCA, July 17--August 3, 1972},
    EDITOR = {Kuyk, Willem and Serre, J.-P.},
      NOTE = {Lecture Notes in Mathematics, Vol. 350},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {1973},
     PAGES = {iv+350},
   MRCLASS = {10D05 (14K22)},
  MRNUMBER = {MR0323724 (48 \#2080)},
}

@article {malle:distro,
    AUTHOR = {Malle, G.},
     TITLE = {On the distribution of {G}alois groups},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {92},
      YEAR = {2002},
    NUMBER = {2},
     PAGES = {315--329},
      ISSN = {0022-314X},
     CODEN = {JNUTA9},
   MRCLASS = {12F12 (11R32 11R47 12F10)},
  MRNUMBER = {MR1884706 (2002k:12010)},
MRREVIEWER = {Helmut V{\"o}lklein},
}


 
@article {malle:distro2,
    AUTHOR = {Malle, G.},
     TITLE = {On the distribution of {G}alois groups. {II}},
   JOURNAL = {Experiment. Math.},
  FJOURNAL = {Experimental Mathematics},
    VOLUME = {13},
      YEAR = {2004},
    NUMBER = {2},
     PAGES = {129--135},
      ISSN = {1058-6458},
   MRCLASS = {11R32 (11R47 12F10)},
  MRNUMBER = {MR2068887 (2005g:11216)},
MRREVIEWER = {F. Diaz y Diaz},
}

@incollection {cohen-diaz-olivier:disc,
    AUTHOR = {Cohen, Henri and Diaz y Diaz, Francisco and Olivier, Michel},
     TITLE = {Counting discriminants of number fields of degree up to four},
 BOOKTITLE = {Algorithmic number theory (Leiden, 2000)},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {1838},
     PAGES = {269--283},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {2000},
   MRCLASS = {11R29 (11R21 11Y40)},
  MRNUMBER = {MR1850611 (2002g:11148)},
MRREVIEWER = {Joe P. Buhler},
}




@article {delaunay:heuristics,
    AUTHOR = {Delaunay, Christophe},
     TITLE = {Heuristics on {T}ate-{S}hafarevitch groups of elliptic curves
              defined over {$\Bbb Q$}},
   JOURNAL = {Experiment. Math.},
  FJOURNAL = {Experimental Mathematics},
    VOLUME = {10},
      YEAR = {2001},
    NUMBER = {2},
     PAGES = {191--196},
      ISSN = {1058-6458},
   MRCLASS = {11G05 (11R29 11R45)},
  MRNUMBER = {MR1837670 (2003a:11065)},
MRREVIEWER = {M. Ram Murty},
}

@proceedings {MR1850596,
     TITLE = {Algorithmic number theory},
    SERIES = {Lecture Notes in Computer Science},
    VOLUME = {1838},
 BOOKTITLE = {Proceedings of the 4th International Symposium (ANTS-IV) held
              at the Universiteit Leiden, Leiden, July 2--7, 2000},
    EDITOR = {Bosma, Wieb},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {2000},
     PAGES = {x+613},
      ISBN = {3-540-67695-3},
   MRCLASS = {11-06 (11Yxx)},
  MRNUMBER = {MR1850596 (2002d:11002)},
}


@incollection {elkies:ants4,
    AUTHOR = {Elkies, N.\thinspace{}D.},
     TITLE = {Rational points near curves and small nonzero {$\vert x\sp
              3-y\sp 2\vert $} via lattice reduction},
 BOOKTITLE = {Algorithmic number theory (Leiden, 2000)},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {1838},
     PAGES = {33--63},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {2000},
MRREVIEWER = {R. C. Baker},
}


@article{rank4,
   author={Jorza, A. and Balakrishna, J. and Stein, W.},
   title = {The {S}mallest {C}onductor for an {E}lliptic {C}urve of {R}ank 
  {F}our is {C}omposite},
   year = {2003},
   journal={{\tt http://wstein.org/rank4/}}

}

@article{cremona-watkins:lattice-distro,
   author={Cremona, J. and Watkins, M.},
   title={Lattice {D}istribution of {M}ordell-{W}eil {G}roups of {E}lliptic {C}urves},
   journal={In Preparation}
}


@article{watkins:cubic,
   author={Watkins, M.},
   title={Rank distribution in a family of cubic twists},
   year={2004},
   journal={{\tt http://www.arxiv.org/abs/math.NT/0412427}}
}

@article{connell:echb,
   author = {Connell, I.},
   title = {The {E}lliptic {C}urves {H}andbook,\\
{\tt http://www.math.mcgill.ca/connell/public/ECH1/}},
   year = {2005}
}

@article{bhargava:density,
   author = {Bhargava, M.},
   title = {The density of discriminants of quartic rings and fields},
   VOLUME = {162},
   number = {2},
   year = {2005},
   journal = {Annals of Mathematics}
}

@article{bsdalg1,
    author={G.~Grigorov and A.~Jorza and S.~Patrikis and C.~Tarnita and W.~Stein},
    title={Computational verification of the {B}irch and {S}winnerton-{D}yer conjecture for individual elliptic curves},
    year = {2009},
   volume = {78}, 
   pages = {2397--2425},
   journal = {Math. Comp.},
   note = {\url{http://wstein.org/papers/bsdalg/}}
}

@article{matplotlib,
   author = {John Hunter},
   title = {matplotlib: {P}ython software for drawing graphs},
   year = {2005},
   journal = {{\tt http://matplotlib.sourceforge.net/}}
}

@incollection {zhang:gzgl2,
    AUTHOR = {Zhang, Shou-Wu},
     TITLE = {Gross-{Z}agier formula for {$\rm GL(2)$}. {II}},
 BOOKTITLE = {Heegner points and Rankin $L$-series},
    SERIES = {Math. Sci. Res. Inst. Publ.},
    VOLUME = {49},
     PAGES = {191--214},
 PUBLISHER = {Cambridge Univ. Press},
   ADDRESS = {Cambridge},
      YEAR = {2004},
   MRCLASS = {11G40 (11F66)},
  MRNUMBER = {MR2083213},
}



@article{stoll:3descent,
   author = {Stoll, M.},
   title = {Explicit $3$-Descent in {M}agma\\
{\tt http://www.faculty.iu-bremen.de/stoll/magma/explicit-3descent/}},
   year = {2005}
}

@article{prickett:phd,
   author = {Prickett, M.},
   title = {Saturation of {M}ordell-{W}eil {G}roups of {E}lliptic {C}urves over
{N}umber {F}ields},
   year = {2004},
   journal = {U. Nottingham, Ph.D. thesis\\
{\tt http://etheses.nottingham.ac.uk/archive/00000052/}}
}
  

@article{pacetti-villegas-p2,
   author = {Pacetti, A. and Rodriguez-Villegas, F.},
   title = {Computing {W}eight 2 {M}odular {F}orms of {L}evel $p^2$},
   year = {2004},
   volume = {74},
   number = {251},
   pages = {1545--1557},
   journal = {Math. Comp.}
}

@article {dembele:hilbert5,
    AUTHOR = {Demb{\'e}l{\'e}, Lassina},
     TITLE = {Explicit computations of {H}ilbert modular forms on {${\Bbb
              Q}(\sqrt{5})$}},
   JOURNAL = {Experiment. Math.},
  FJOURNAL = {Experimental Mathematics},
    VOLUME = {14},
      YEAR = {2005},
    NUMBER = {4},
     PAGES = {457--466},
      ISSN = {1058-6458},
   MRCLASS = {11F41 (11Y16)},
  MRNUMBER = {MR2193808},
MRREVIEWER = {Alexandru E. Ghitza},
}


@article{grigor:phd,
   author = {Grigorov, G.},
   title = {{K}ato's {E}uler {S}ystem and the {M}ain {C}onjecture},
    journal = {Harvard {P}h.{D}. {T}hesis},
   year = {2005}
}

@article {ono-skinner:nonvanish,
    AUTHOR = {Ono, Ken and Skinner, Christopher},
     TITLE = {Non-vanishing of quadratic twists of modular {$L$}-functions},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {134},
      YEAR = {1998},
    NUMBER = {3},
     PAGES = {651--660},
      ISSN = {0020-9910},
     CODEN = {INVMBH},
   MRCLASS = {11F67 (11G40)},
  MRNUMBER = {MR1660945 (2000a:11077)},
MRREVIEWER = {A. Perelli},
}


@article {ono:nonvanish_twist,
    AUTHOR = {Ono, Ken},
     TITLE = {Nonvanishing of quadratic twists of modular {$L$}-functions
              and applications to elliptic curves},
   JOURNAL = {J. Reine Angew. Math.},
  FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik},
    VOLUME = {533},
      YEAR = {2001},
     PAGES = {81--97},
      ISSN = {0075-4102},
     CODEN = {JRMAA8},
   MRCLASS = {11F67 (11G05 11G40)},
  MRNUMBER = {MR1823865 (2002a:11051)},
MRREVIEWER = {Vinayak Vatsal},
}


@article {waldspurger:valeurs,
    AUTHOR = {Waldspurger, J.-L.},
     TITLE = {Sur les valeurs de certaines fonctions {$L$} automorphes en
              leur centre de sym\'etrie},
   JOURNAL = {Compositio Math.},
  FJOURNAL = {Compositio Mathematica},
    VOLUME = {54},
      YEAR = {1985},
    NUMBER = {2},
     PAGES = {173--242},
      ISSN = {0010-437X},
     CODEN = {CMPMAF},
   MRCLASS = {11F70 (11F67 22E55)},
  MRNUMBER = {MR783511 (87g:11061b)},
MRREVIEWER = {Stephen Gelbart},
}
@article {waldspurger:gl2,
    AUTHOR = {Waldspurger, J.-L.},
     TITLE = {Quelques propri\'et\'es arithm\'etiques de certaines formes
              automorphes sur {${\rm GL}(2)$}},
   JOURNAL = {Compositio Math.},
  FJOURNAL = {Compositio Mathematica},
    VOLUME = {54},
      YEAR = {1985},
    NUMBER = {2},
     PAGES = {121--171},
      ISSN = {0010-437X},
     CODEN = {CMPMAF},
   MRCLASS = {11F70 (22E55)},
  MRNUMBER = {MR783510 (87g:11061a)},
MRREVIEWER = {Stephen Gelbart},
}


@article {gonzalez:bsd,
    AUTHOR = {Gonzalez-Avil{\'e}s, Cristian D.},
     TITLE = {On the conjecture of {B}irch and {S}winnerton-{D}yer},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {349},
      YEAR = {1997},
    NUMBER = {10},
     PAGES = {4181--4200},
      ISSN = {0002-9947},
     CODEN = {TAMTAM},
   MRCLASS = {11G40 (11G05)},
  MRNUMBER = {MR1390036 (98c:11062)},
MRREVIEWER = {Eric Liverance},
}

@article {mazur-rubin:kolyvagin_systems,
    AUTHOR = {Mazur, Barry and Rubin, Karl},
     TITLE = {Kolyvagin systems},
   JOURNAL = {Mem. Amer. Math. Soc.},
  FJOURNAL = {Memoirs of the American Mathematical Society},
    VOLUME = {168},
      YEAR = {2004},
    NUMBER = {799},
     PAGES = {viii+96},
      ISSN = {0065-9266},
     CODEN = {MAMCAU},
   MRCLASS = {11R34 (11F80 11G40 11R23)},
  MRNUMBER = {MR2031496 (2005b:11179)},
MRREVIEWER = {Thomas A. Weston},
}

@article {matsuno:finitelambda,
    AUTHOR = {Matsuno, Kazuo},
     TITLE = {Finite {$\Lambda$}-submodules of {S}elmer groups of abelian
              varieties over cyclotomic {$\mathbb Z\sb p$}-extensions},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {99},
      YEAR = {2003},
    NUMBER = {2},
     PAGES = {415--443},
      ISSN = {0022-314X},
     CODEN = {JNUTA9},
   MRCLASS = {11G10},
  MRNUMBER = {MR1969183 (2004c:11098)},
MRREVIEWER = {Ivica Gusi{\'c}},
}

@article{jorza:seniorthesis,
   AUTHOR = {Jorza, A.},
   TITLE = {The {B}irch and {S}winnerton-{D}yer {C}onjecture for {A}belian 
   {V}arieties over {N}umber {F}ields},
   journal = {Harvard University Senior Thesis},
    year= {2005}
}

@article{ribet:congrel,
    AUTHOR = {Ribet, Kenneth A.},
     TITLE = {Congruence relations between modular forms},
 JOURNAL = {Proc. International Congress of Mathematicians},
     PAGES = {503--514},
      YEAR = {1983}
}

}

@book {darmon:ratpoints,
    AUTHOR = {Darmon, Henri},
     TITLE = {Rational points on modular elliptic curves},
    SERIES = {CBMS Regional Conference Series in Mathematics},
    VOLUME = {101},
 PUBLISHER = {Published for the Conference Board of the Mathematical
              Sciences, Washington, DC},
      YEAR = {2004},
     PAGES = {xii+129},
      ISBN = {0-8218-2868-1},
   MRCLASS = {11G40 (11F67 11F85 11G05 11G18)},
  MRNUMBER = {MR2020572 (2004k:11103)},
MRREVIEWER = {Chandrashekhar Khare},
}

@article {kedlaya:counting_mw,
    AUTHOR = {Kedlaya, Kiran S.},
     TITLE = {Counting points on hyperelliptic curves using
              {M}onsky-{W}ashnitzer cohomology},
   JOURNAL = {J. Ramanujan Math. Soc.},
  FJOURNAL = {Journal of the Ramanujan Mathematical Society},
    VOLUME = {16},
      YEAR = {2001},
    NUMBER = {4},
     PAGES = {323--338},
      ISSN = {0970-1249},
   MRCLASS = {14G05 (11G25 14F43 14G15)},
  MRNUMBER = {MR1877805 (2002m:14019)},
MRREVIEWER = {Miriam D. Abd{\'o}n},
}


@article {katz:padic_interp,
    AUTHOR = {Katz, Nicholas M.},
     TITLE = {{$p$}-adic interpolation of real analytic {E}isenstein series},
   JOURNAL = {Ann. of Math. (2)},
    VOLUME = {104},
      YEAR = {1976},
    NUMBER = {3},
     PAGES = {459--571},
   MRCLASS = {14G10 (10D25)},
  MRNUMBER = {MR0506271 (58 \#22071)},
MRREVIEWER = {V. V. Sokurov},
}

@article{cojocaru-kani:surj,
       AUTHOR = {Cojocaru, Alina Carmen and Kani, Ernst},
   TITLE = {On the surjectivity of the Galois representations associated to
non-CM elliptic curves}
}

@article {cojocaru-kani,
    AUTHOR = {Cojocaru, Alina Carmen and Kani, Ernst},
     TITLE = {The modular degree and the congruence number of a weight 2
              cusp form},
   JOURNAL = {Acta Arith.},
  FJOURNAL = {Acta Arithmetica},
    VOLUME = {114},
      YEAR = {2004},
    NUMBER = {2},
     PAGES = {159--167},
      ISSN = {0065-1036},
     CODEN = {AARIA9},
   MRCLASS = {11F33 (11F11 11G18)},
  MRNUMBER = {MR2068855},
MRREVIEWER = {Siman Wong},
}


@article {stein-watkins:ns,
    AUTHOR = {Stein, W. and Watkins, M.},
     TITLE = {Modular parametrizations of {N}eumann-{S}etzer elliptic
              curves},
   JOURNAL = {Int. Math. Res. Not.},
  FJOURNAL = {International Mathematics Research Notices},
      YEAR = {2004},
    NUMBER = {27},
     PAGES = {1395--1405},
      ISSN = {1073-7928},
   MRCLASS = {11G05 (11G18)},
  MRNUMBER = {MR2052021 (2005c:11070)},
MRREVIEWER = {Siman Wong},
}


@incollection {cohen-lenstra:heuristics,
    AUTHOR = {Cohen, H. and Lenstra, Jr., H. W.},
     TITLE = {Heuristics on class groups of number fields},
 BOOKTITLE = {Number theory, Noordwijkerhout 1983 (Noordwijkerhout, 1983)},
    SERIES = {Lecture Notes in Math.},
    VOLUME = {1068},
     PAGES = {33--62},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {1984},
   MRCLASS = {11R29 (13C13)},
  MRNUMBER = {MR756082 (85j:11144)},
MRREVIEWER = {F. J. van der Linden},
}

@proceedings {MR756078,
     TITLE = {Number theory, {N}oordwijkerhout 1983},
    SERIES = {Lecture Notes in Mathematics},
    VOLUME = {1068},
 BOOKTITLE = {Proceedings of the thirteenth Journ\'ees Arithm\'etiques held
              at Noordwijkerhout, July 11--15, 1983},
    EDITOR = {Jager, H.},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {1984},
     PAGES = {v+296},
      ISBN = {3-540-13356-9},
   MRCLASS = {11-06},
  MRNUMBER = {MR756078 (85i:11001)},
}

@article {zhang:gz_formulas,
    AUTHOR = {Zhang, Shou-Wu},
     TITLE = {Gross-{Z}agier formula for {${\rm GL}\sb 2$}},
   JOURNAL = {Asian J. Math.},
  FJOURNAL = {The Asian Journal of Mathematics},
    VOLUME = {5},
      YEAR = {2001},
    NUMBER = {2},
     PAGES = {183--290},
      ISSN = {1093-6106},
   MRCLASS = {11G18 (11F67 11G50 14G35)},
  MRNUMBER = {MR1868935 (2003k:11101)},
MRREVIEWER = {Douglas L. Ulmer}
}

@article {buchmann_lenstra:approx,
    AUTHOR = {Buchmann, J. A. and Lenstra, Jr., H. W.},
     TITLE = {Approximating rings of integers in number fields},
   JOURNAL = {J. Th\'eor. Nombres Bordeaux},
  FJOURNAL = {Journal de Th\'eorie des Nombres de Bordeaux},
    VOLUME = {6},
      YEAR = {1994},
    NUMBER = {2},
     PAGES = {221--260},
      ISSN = {1246-7405},
   MRCLASS = {11R04 (11Y40)},
  MRNUMBER = {MR1360644 (96m:11092)},
MRREVIEWER = {Joe P. Buhler}
}

@article{zagier:primes50,
   author = {Zagier, D.},
   title = {The First 50 Million Prime Numbers},
   year = {1975},
   note = {{\tt http://wstein.org/scans/papers/zagier/}}
}

@book{stein:ent,
   author = {Stein, W.},
   title = {Elementary {N}umber {T}heory,\\
{\tt http://wstein.org/ent/}},
   year = {2005}
}

@article{rsa, 
   author = {RSA Security Solutions}, 
   title = {{\tt http://www.rsasecurity.com/}}
}

@article{mazur-rubin:large_selmer,
   author = {Rubin, K. and Mazur, B.},
   title = {Finding Large Selmer Groups},
   year = {2005},
   note = {in preparation}
}

@article{jetchev-stein:higher,
   author = {Jetchev, D. and Stein, W.},
    title = {Visibility of {S}hafarevich-{T}ate {G}roups at {H}igher {L}evel},
    year = {2005},
    note = {in preparation}
}

@article {mazur-ribet,
    AUTHOR = {Mazur, B. and Ribet, K. A.},
     TITLE = {Two-dimensional representations in the arithmetic of modular
              curves},
      NOTE = {Courbes modulaires et courbes de Shimura (Orsay, 1987/1988)},
   JOURNAL = {Ast\'erisque},
  FJOURNAL = {Ast\'erisque},
    NUMBER = {196-197},
      YEAR = {1991},
     PAGES = {6, 215--255 (1992)},
      ISSN = {0303-1179},
   MRCLASS = {11F80 (11F25 11G18)},
  MRNUMBER = {MR1141460 (93d:11056)},
MRREVIEWER = {Jacques Tilouine},
}

 
@incollection {ribet:comp,
    AUTHOR = {Ribet, Kenneth A.},
     TITLE = {On the component groups and the {S}himura subgroup of {$J\sb
              0(N)$}},
 BOOKTITLE = {S\'eminaire de Th\'eorie des Nombres, 1987--1988 (Talence,
              1987--1988)},
     PAGES = {Exp.\ No.\ 6, 10},
 PUBLISHER = {Univ. Bordeaux I},
   ADDRESS = {Talence},
      YEAR = {19??},
   MRCLASS = {11G05 (11F11)},
  MRNUMBER = {MR993107 (91b:11070)},
}

 
@book {MR993101,
     TITLE = {S\'eminaire de {T}h\'eorie des {N}ombres. 1987--1988},
      NOTE = {Held at the Universit\'e de Bordeaux I, Talence, 1987--1988},
 PUBLISHER = {Universit\'e de Bordeaux I U.E.R. de Math\'ematiques et
              d'Informatique Laboratoire de Th\'eorie des Nombres},
   ADDRESS = {Talence},
      YEAR = {19??},
     PAGES = {vi+536},
   MRCLASS = {11-06},
  MRNUMBER = {MR993101 (90a:11003)},
}



@article {cremona-lingham,
  author = {Cremona, J. and Lingham, M.\thinspace{}P.},
  title = {Finding all elliptic curves with good reduction 
outside a given set of primes},
   year = {2004},
   journal = {In Progress}
}
 
@article {rubin-silverberg:ranks,
    AUTHOR = {Rubin, K. and Silverberg, A.},
     TITLE = {Ranks of elliptic curves},
   JOURNAL = {Bull. Amer. Math. Soc. (N.S.)},
  FJOURNAL = {American Mathematical Society. Bulletin. New Series},
    VOLUME = {39},
      YEAR = {2002},
    NUMBER = {4},
     PAGES = {455--474 (electronic)},
      ISSN = {0273-0979},
     CODEN = {BAMOAD},
   MRCLASS = {11G05 (11G40)},
  MRNUMBER = {MR1920278 (2003f:11080)},
MRREVIEWER = {Ioannis Papadopoulos},
}

 
@incollection {silverberg:open_questions,
    AUTHOR = {Silverberg, A.},
     TITLE = {Open questions in arithmetic algebraic geometry},
 BOOKTITLE = {Arithmetic algebraic geometry (Park City, UT, 1999)},
    SERIES = {IAS/Park City Math. Ser.},
    VOLUME = {9},
     PAGES = {83--142},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, RI},
      YEAR = {2001},
   MRCLASS = {11Gxx (14Gxx)},
  MRNUMBER = {MR1860041 (2002g:11073)},
MRREVIEWER = {Joseph H. Silverman},
}

@book {MR1860012,
     TITLE = {Arithmetic algebraic geometry},
    SERIES = {IAS/Park City Mathematics Series},
    VOLUME = {9},
    EDITOR = {Conrad, Brian and Rubin, Karl},
      NOTE = {Including papers from the Graduate Summer School of the
              Institute for Advanced Study/Park City Mathematics Institute
              held in Park City, UT, June 20--July 10, 1999},
 PUBLISHER = {American Mathematical Society},
   ADDRESS = {Providence, RI},
      YEAR = {2001},
     PAGES = {xiv+569},
      ISBN = {0-8218-2173-3},
   MRCLASS = {11-06 (14-06)},
  MRNUMBER = {MR1860012 (2002d:11003)},
}


@incollection {goldfeld:conjectures_quadratic,
    AUTHOR = {Goldfeld, D.},
     TITLE = {Conjectures on elliptic curves over quadratic fields},
 BOOKTITLE = {Number theory, Carbondale 1979 (Proc. Southern Illinois Conf.,
              Southern Illinois Univ., Carbondale, Ill., 1979)},
    SERIES = {Lecture Notes in Math.},
    VOLUME = {751},
     PAGES = {108--118},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {1979},
   MRCLASS = {12A70 (14K07)},
  MRNUMBER = {MR564926 (81i:12014)},
MRREVIEWER = {Kenneth Kramer},
}

 
@proceedings {MR564918,
     TITLE = {Number theory, {C}arbondale 1979},
    SERIES = {Lecture Notes in Mathematics},
    VOLUME = {751},
 BOOKTITLE = {Proceedings of the Southern Illinois Number Theory Conference,
              held at Southern Illinois University, Carbondale, Ill., March
              30--31, 1979},
    EDITOR = {Nathanson, Melvyn B.},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {1979},
     PAGES = {iv+342},
      ISBN = {3-540-09559-4},
   MRCLASS = {10-06},
  MRNUMBER = {MR564918 (81a:10004)},
}


@article {kramarz-zagier,
    AUTHOR = {Zagier, D. and Kramarz, G.},
     TITLE = {Numerical investigations related to the {$L$}-series of
              certain elliptic curves},
   JOURNAL = {J. Indian Math. Soc. (N.S.)},
  FJOURNAL = {The Journal of the Indian Mathematical Society. New Series},
    VOLUME = {52},
      YEAR = {1987},
     PAGES = {51--69 (1988)},
      ISSN = {0019-5839},
     CODEN = {JIMTA2},
   MRCLASS = {11G05 (11G40 11Y50)},
  MRNUMBER = {MR989230 (90d:11072)},
MRREVIEWER = {M. Ram Murty},
}

@article{darmon-pollack,
  author = {Darmon, H. and Pollack, R.}, 
  title = {The efficient calculation of {S}tark-{H}eegner points
via overconvergent modular symbols},
   year = {2004}
}

@article{kraus,
  author = {Kraus, Alain},
  title = {D\'etermination du poids et du conducteur associ\'es
aux repr\'esentations des points de $p$-torsion d'une courbe elliptique}
}

@article{math252,
  author = {Stein, W.},
  title = {Modular Abelian Varieties, \hfill\mbox{}
{\tt http://wstein.org/edu/Fall2003/252/}},
  year = {2003}
}

@article{dembele,
  author = {Dembele, Lassina},
  title = {Quaternionic Modular Symbols and Computing {H}ilbert Modular Forms,
\hfill\mbox{}
{\tt http://wstein.org/mcs/archive/Spring2004/dembele.html}},
  year = {2004}
}

@article{lemelin:dominic,
  author = {Lemelin, Dominic},
  title = {Mazur-Tate Type Conjectures for Elliptic Curves Defined over Quadratic Imaginary Fields},
  year = {2001}
}

@article{martin:thesis,
  author = {Martin, François},
  title = {P\'eriodes de formes modulaires de poids 1},
  year = {2001},
 journal = {{\tt http://wstein.org/scans/papers/diderot/}}
}
  

@article{basmaji:thesis,
   author = {Basmaji, Jacques},
   TITLE = {Ein Algorithmus zur Berechnung von Hecke-Operatoren und
            Anwendungen auf modulare Kurven},
   YEAR = {1996},
   journal={{\tt http://wstein.org/scans/papers/basmaji/}}
}

@article {sokurov:shimura,
    AUTHOR = {{\v{S}}okurov, V.\thinspace{}V.},
     TITLE = {Shimura integrals of cusp forms},
   JOURNAL = {Izv. Akad. Nauk SSSR Ser. Mat.},
  FJOURNAL = {Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya},
    VOLUME = {44},
      YEAR = {1980},
    NUMBER = {3},
     PAGES = {670--718, 720},
      ISSN = {0373-2436},
   MRCLASS = {10D12 (14K22)},
  MRNUMBER = {MR582162 (82b:10029)},
MRREVIEWER = {K.-B. Gundlach},
}

@book {knuth2,
    AUTHOR = {Knuth, Donald E.},
     TITLE = {The art of computer programming. {V}ol. 2},
   EDITION = {Third},
      NOTE = {Seminumerical algorithms,
              Addison-Wesley Series in Computer Science and Information
              Processing},
 PUBLISHER = {Addison-Wesley Publishing Co., Reading, Mass.}
}

@Article{	  csirik-wetherell-zieve:g0,
  author	= {Csirik, Janos A. and Wetherell, Joseph L. and Zieve,
		  Michael E.},
  title		= {On the genera of {$X_0(N)$}},
  journal	= {See {\tt http://www.csirik.net/papers.html}},
  year		= {2001}
}

@Article{	  pr:exp,
  author	= {Perrin-Riou, Bernadette},
  title		= {Arithm\'etique des courbes elliptiques \`a r\'eduction
		  supersinguli\`ere en {$p$}},
  journal	= {Experiment. Math.},
  fjournal	= {Experimental Mathematics},
  volume	= {12},
  year		= {2003},
  number	= {2},
  pages		= {155--186},
  issn		= {1058-6458},
  mrclass	= {11G05},
  mrnumber	= {MR2016704}
}

@Article{	  mtt,
  author	= {Mazur, B. and Tate, J. and Teitelbaum, J.},
  title		= {On {$p$}-adic analogues of the conjectures of {B}irch and
		  {S}winnerton-{D}yer},
  journal	= {Invent. Math.},
  fjournal	= {Inventiones Mathematicae},
  volume	= {84},
  year		= {1986},
  number	= {1},
  pages		= {1--48},
  issn		= {0020-9910},
  coden		= {INVMBH},
  mrclass	= {11G40 (11G05 14G10)},
  mrnumber	= {MR830037 (87e:11076)},
  mrreviewer	= {Kenneth A. Ribet}
}

@Article{	  serre:asymptotique,
  author	= {Serre, Jean-Pierre},
  title		= {R\'epartition asymptotique des valeurs propres de
		  l'op\'erateur de {H}ecke {$T\sb p$}},
  journal	= {J. Amer. Math. Soc.},
  fjournal	= {Journal of the American Mathematical Society},
  volume	= {10},
  year		= {1997},
  number	= {1},
  pages		= {75--102},
  issn		= {0894-0347},
  mrclass	= {11F30 (11F25 11G20 11N37 11R45)},
  mrnumber	= {97h:11048},
  mrreviewer	= {Glenn Stevens}
}

@Book{		  iwaniec:topics,
  author	= {Iwaniec, Henryk},
  title		= {Topics in classical automorphic forms},
  series	= {Graduate Studies in Mathematics},
  volume	= {17},
  publisher	= {American Mathematical Society},
  address	= {Providence, RI},
  year		= {1997},
  pages		= {xii+259},
  isbn		= {0-8218-0777-3},
  mrclass	= {11Fxx (11-02)},
  mrnumber	= {98e:11051},
  mrreviewer	= {B. Ramakrishnan}
}

@Article{	  gordon:dlp,
  author	= {Gordon, D.},
  year	= {2004},
  title		= {Discrete Logarithm Problem, \hfill\\ {\tt
		  http://www.win.tue.nl/\~{ }henkvt/Content.html}}
}

@Proceedings{	  mr98i:94002,
  title		= {Advances in cryptology---{EUROCRYPT} '97},
  series	= {Lecture Notes in Computer Science},
  volume	= {1233},
  booktitle	= {Proceedings of the 16th International Conference on the
		  Theory and Application of Cryptographic Techniques held in
		  Konstanz, May 11--15, 1997},
  editor	= {Fumy, Walter},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1997},
  pages		= {xii+509},
  isbn		= {3-540-62975-0},
  mrclass	= {94-06 (68P25 94A60)},
  mrnumber	= {98i:94002}
}

@Article{	  nechaev:lower,
  author	= {Nechaev, V. I.},
  title		= {On the complexity of a deterministic algorithm for a
		  discrete logarithm},
  journal	= {Mat. Zametki},
  fjournal	= {Rossi\u\i skaya Akademiya Nauk. Matematicheskie Zametki},
  volume	= {55},
  year		= {1994},
  number	= {2},
  pages		= {91--101, 189},
  issn		= {0025-567X},
  mrclass	= {11Y16},
  mrnumber	= {96a:11145}
}

@InCollection{	  shoup:lower,
  author	= {Shoup, Victor},
  title		= {Lower bounds for discrete logarithms and related
		  problems},
  booktitle	= {Advances in cryptology---EUROCRYPT '97 (Konstanz)},
  series	= {Lecture Notes in Comput. Sci.},
  volume	= {1233},
  pages		= {256--266},
  publisher	= {Springer},
  address	= {Berlin},
  year		= {1997},
  mrclass	= {94A60 (68P25 68Q25)},
  mrnumber	= {98j:94023}
}

@Article{	  gordon:dlog,
  author	= {Gordon, Daniel M.},
  title		= {Discrete logarithms in {${\rm GF}(p)$} using the number
		  field sieve},
  journal	= {SIAM J. Discrete Math.},
  fjournal	= {SIAM Journal on Discrete Mathematics},
  volume	= {6},
  year		= {1993},
  number	= {1},
  pages		= {124--138},
  issn		= {0895-4801},
  coden		= {SJDMEC},
  mrclass	= {11Y16 (11N36)},
  mrnumber	= {94d:11104},
  mrreviewer	= {Joe P. Buhler}
}

@Article{	  python,
  author	= {Rossum, Guido van},
  title		= {Python,\newline{\tt http://www.python.org}}
}

@article{        cha:vanishing,
   author       = {Cha, Byungchul},
   title        = {Vanishing of some cohomology groups and bounds for the {S}hafarevich-{T}ate groups of elliptic curves},
   journal      = {J. Number Theory.},
   year         = {2005},
   volume       = {111},
   issue        = {1},
   pages        = {154--178},
   date         = {March 2005}
}
 
@Article{	  cha:shabound,
  author	= {Cha, Byungchul},
  title		= {Vanishing of {S}ome {C}ohomology {G}roups and {B}ounds for
		  the {S}hafarevich-{T}ate {G}roups of {E}lliptic {C}urves},
  journal	= {Johns-Hopkins Ph.D. Thesis},
  year		= {2003}
}

@Article{	  cassels:7,
  author	= {Cassels, J. W. S.},
  title		= {Arithmetic on curves of genus 1. {VIII}. {O}n conjectures
		  of {B}irch and {S}winnerton-{D}yer},
  journal	= {J. Reine Angew. Math.},
  volume	= {217},
  year		= {1965},
  pages		= {180--199},
  mrclass	= {14.48 (14.49)},
  mrnumber	= {31 \#3420},
  mrreviewer	= {T. Ono}
}

@Article{	  kedlaya:counting-errata,
  author	= {Kedlaya, K.\thinspace{}S.},
  title		= {Errata for: ``{C}ounting points on hyperelliptic curves
		  using {M}onsky-{W}ashnitzer cohomology'' [{J}. {R}amanujan
		  {M}ath.\ {S}oc.\ {\bf 16} (2001), no. 4, 323--338},
  note		= {Dedicated to Professor K. S. Padmanabhan},
  journal	= {J. Ramanujan Math. Soc.},
  fjournal	= {Journal of the Ramanujan Mathematical Society},
  volume	= {18},
  year		= {2003},
  number	= {4},
  pages		= {417--418},
  issn		= {0970-1249},
  mrclass	= {14G05 (11G25 14F43 14G15)},
  mrnumber	= {2 043 934}
}

@Article{	  abbott:padic,
  author	= {Abbott, J.},
  title		= {Recovery of algebraic numbers from their $p$-adic
		  approximations},
  journal	= {Proceedings of the ACM-SIGSAM 1989 international symposium
		  on Symbolic and algebraic computation},
  pages		= {112--120},
  year		= {1989},
  isbn		= {0-89791-325-6},
  publisher	= {ACM Press, New York, NY, USA}
}

@Article{	  tate:arithmetic,
  author	= {Tate, J.},
  title		= {The arithmetic of elliptic curves},
  journal	= {Invent. Math.},
  volume	= {23},
  year		= {1974},
  pages		= {179--206},
  mrclass	= {10D05 (14G25 14K15)},
  mrnumber	= {54 \#7380},
  mrreviewer	= {A. P. Ogg}
}

@Article{	  mazur-tate:sigma,
  author	= {Mazur, B. and Tate, J.},
  title		= {The {$p$}-adic sigma function},
  journal	= {Duke Math. J.},
  fjournal	= {Duke Mathematical Journal},
  volume	= {62},
  year		= {1991},
  number	= {3},
  pages		= {663--688},
  issn		= {0012-7094},
  coden		= {DUMJAO},
  mrclass	= {11G07 (11S80)},
  mrnumber	= {93d:11059}
}

@Book{		  artin-tate:cft,
  author	= {Artin, E. and Tate, J.},
  title		= {Class field theory},
  series	= {Advanced Book Classics},
  edition	= {Second},
  publisher	= {Addison-Wesley Publishing Company Advanced Book Program},
  address	= {Redwood City, CA},
  year		= {1990},
  pages		= {xxxviii+259},
  isbn		= {0-201-51011-1},
  mrclass	= {11R37 (11-01 11R34)},
  mrnumber	= {91b:11129}
}

@Article{	  mahler:inequalities,
  author	= {Mahler, K.},
  title		= {Inequalities for ideal bases in algebraic number fields},
  journal	= {J. Austral. Math. Soc.},
  volume	= {4},
  year		= {1964},
  pages		= {425--448},
  mrclass	= {12.50},
  mrnumber	= {31 \#1243},
  mrreviewer	= {L. R. McCulloh}
}

@Article{	  iwasawa:adele,
  author	= {Iwasawa, K.},
  title		= {On the rings of valuation vectors},
  journal	= {Ann. of Math. (2)},
  volume	= {57},
  year		= {1953},
  pages		= {331--356},
  mrclass	= {10.0X},
  mrnumber	= {14,849a},
  mrreviewer	= {J. T. Tate}
}

@Book{		  lang:algebraic_numbers,
  author	= {Lang, S.},
  title		= {Algebraic numbers},
  publisher	= {Addison-Wesley Publishing Co., Inc., Reading, Mass.-Palo
		  Alto-London},
  year		= {1964},
  pages		= {ix+163},
  mrclass	= {10.65},
  mrnumber	= {28 \#3974},
  mrreviewer	= {S. Chowla}
}

@Book{		  cassels:lectures,
  author	= {Cassels, J.\thinspace{}W.\thinspace{}S.},
  title		= {Lectures on elliptic curves},
  series	= {London Mathematical Society Student Texts},
  volume	= {24},
  publisher	= {Cambridge University Press},
  address	= {Cambridge},
  year		= {1991},
  pages		= {vi+137},
  isbn		= {0-521-41517-9; 0-521-42530-1},
  mrclass	= {11G05 (14H52)},
  mrnumber	= {92k:11058},
  mrreviewer	= {Philippe Satg{\'e}}
}

@Article{	  lenstra:pell,
  author	= {Lenstra, Jr., H.\thinspace{}W.},
  title		= {Solving the {P}ell equation},
  journal	= {Notices Amer. Math. Soc.},
  fjournal	= {Notices of the American Mathematical Society},
  volume	= {49},
  year		= {2002},
  number	= {2},
  pages		= {182--192},
  issn		= {0002-9920},
  coden		= {AMNOAN},
  mrclass	= {11D09 (01A99 11R27)},
  mrnumber	= {2002i:11028},
  mrreviewer	= {Duncan A. Buell}
}

@Book{		  artin:algebra,
  author	= {Artin, M.},
  title		= {Algebra},
  publisher	= {Prentice Hall Inc.},
  address	= {Englewood Cliffs, NJ},
  year		= {1991},
  pages		= {xviii+618},
  isbn		= {0-13-004763-5},
  mrclass	= {00A05 (11-01 12-01 13-01 15-01 16-01 20-01)},
  mrnumber	= {92g:00001},
  mrreviewer	= {Gerald J. Janusz}
}

@Book{		  artin:ant,
  author	= {Artin, E.},
  title		= {Theory of algebraic numbers},
  series	= {Notes by Gerhard W\"urges from lectures held at the
		  Mathematisches Institut, G\"ottingen, Germany, in the
		  Winter Semester},
  volume	= {1956/7},
  publisher	= {George Striker, Schildweg 12, G\"ottingen},
  year		= {1959},
  pages		= {172},
  mrclass	= {10.65},
  mrnumber	= {24 \#A1884},
  mrreviewer	= {L. Carlitz}
}

@Book{		  am,
  author	= {Atiyah, M. F. and Macdonald, I. G.},
  title		= {Introduction to commutative algebra},
  publisher	= {Addison-Wesley Publishing Co., Reading, Mass.-London-Don
		  Mills, Ont.},
  year		= {1969},
  pages		= {ix+128},
  mrclass	= {13.00},
  mrnumber	= {39 \#4129},
  mrreviewer	= {J. A. Johnson}
}

@Article{	  agashe,
  author	= {Agashe, A.},
  title		= {On invisible elements of the {T}ate-{S}hafarevich group},
  journal	= {C. R. Acad. Sci. Paris S\'er. I Math.},
  fjournal	= {Comptes Rendus de l'Acad\'emie des Sciences. S\'erie I.
		  Math\'ematique},
  volume	= {328},
  year		= {1999},
  number	= {5},
  pages		= {369--374},
  issn		= {0764-4442},
  coden		= {CASMEI},
  mrclass	= {11Gxx},
  mrnumber	= {1 678 131}
}

@article {agashe-stein:bsd,
    AUTHOR = {Agashe, A. and Stein, W.},
     TITLE = {Visible evidence for the {B}irch and {S}winnerton-{D}yer
              conjecture for modular abelian varieties of analytic rank
              zero},
      NOTE = {With an appendix by J.\ Cremona and B.\ Mazur},
   JOURNAL = {Math. Comp.},
  FJOURNAL = {Mathematics of Computation},
    VOLUME = {74},
      YEAR = {2005},
    NUMBER = {249},
     PAGES = {455--484 (electronic)},
      ISSN = {0025-5718},
     CODEN = {MCMPAF},
   MRCLASS = {11G40 (11G10)},
  MRNUMBER = {2085902},
}


@Article{	  agashe-ribet-stein:manin,
  author	= "Agashe, A. and Ribet, K.\thinspace{}A. and 
                    Stein, W.\thinspace{}A.",
  title		= "The {M}anin {C}onstant",
  year		= {2006},
  journal	= {JPAM Coates Volume},
  note = {\url{http://wstein.org/papers/ars-manin/}}
}

@Article{	  agashe-ribet-stein:modular,
  author	= "Agashe, A. and Ribet, K.\thinspace{}A. and 
                    Stein, W.\thinspace{}A.",
  title		= "The {M}odular {D}egree, {C}ongruence {P}rimes 
and {M}ultiplicity {O}ne",
  year		= {2006},
  journal	= {IMRN Coates Volume},
  note = {\url{http://wstein.org/papers/ars-congruence/}}
}

@article {lario-schoof,
    AUTHOR = {Lario, Joan-C. and Schoof, Ren{\'e}},
     TITLE = {Some computations with {H}ecke rings and deformation rings},
      NOTE = {With an appendix by Amod Agashe and William Stein},
   JOURNAL = {Experiment. Math.},
  FJOURNAL = {Experimental Mathematics},
    VOLUME = {11},
      YEAR = {2002},
    NUMBER = {2},
     PAGES = {303--311},
      ISSN = {1058-6458},
   MRCLASS = {11F80 (11F11 11F25)},
  MRNUMBER = {MR1959271 (2004b:11072)},
MRREVIEWER = {Lea Terracini},
}


@Article{	  agashe-stein:visibility,
  author	= {Agashe, A. and Stein, W.},
  title		= {Visibility of {S}hafarevich-{T}ate groups of abelian
		  varieties},
  journal	= {J. Number Theory},
  fjournal	= {Journal of Number Theory},
  volume	= {97},
  year		= {2002},
  number	= {1},
  pages		= {171--185},
  issn		= {0022-314X},
  coden		= {JNUTA9},
  mrclass	= {11G40 (11G10 14K15)},
  mrreviewer	= {Chandan Singh Dalawat}
}

@Article{	  agashe:invisible,
  author	= {Agash{\'e}, Amod},
  title		= {On invisible elements of the {T}ate-{S}hafarevich group},
  journal	= {C. R. Acad. Sci. Paris S\'er. I Math.},
  fjournal	= {Comptes Rendus de l'Acad\'emie des Sciences. S\'erie I.
		  Math\'ematique},
  volume	= {328},
  year		= {1999},
  number	= {5},
  pages		= {369--374},
  issn		= {0764-4442},
  coden		= {CASMEI},
  mrclass	= {11G40 (11G10 11G18)},
  mrnumber	= {2000e:11083},
  mrreviewer	= {Kenneth Kramer}
}

@Article{	  agashe:phd,
  author	= "Agashe, A.",
  title		= {The {B}irch and {S}winnerton-{D}yer formula for modular
		  abelian varieties of analytic rank~$0$},
  journal	= {Ph.D. thesis, University of California, Berkeley},
  year		= {2000}
}

@Book{		  antwerpiv,
  title		= {Modular functions of one variable. {I}{V}},
  booktitle	= {Proceedings of the International Summer School on Modular
		  Functions of One Variable and Arithmetical Applications,
		  RUCA, University of Antwerp, Antwerp, July 17--August 3,
		  1972},
  editor	= {Birch, B.\thinspace{}J. and Kuyk, W.},
  note		= {Lecture Notes in Mathematics, Vol. 476},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1975},
  pages		= {iv+151}
}

@Article{	  artin:conjecture,
  author	= {Artin, E.},
  title		= {{\"U}ber eine neue {A}rt von {L}-Reihen},
  journal	= {Abh. Math. Sem. Univ. Hamburg},
  volume	= {3},
  year		= {1923},
  pages		= {89--108}
}

@Article{	  artin:conjecture2,
  author	= {Artin, E},
  title		= {Zur {T}heorie der {L}-{R}eihen mit allgemeinen
		  {G}ruppencharakteren},
  journal	= {Abh. math. Semin. Univ. Hamburg},
  volume	= {8},
  year		= {1930},
  pages		= {292--306}
}

@Article{	  ash-stevens,
  author	= {Ash, A. and Stevens, G.},
  title		= {Cohomology of arithmetic groups and congruences between
		  systems of {H}ecke eigenvalues},
  journal	= {J. Reine Angew. Math.},
  fjournal	= {Journal f\"ur die Reine und Angewandte Mathematik},
  volume	= {365},
  year		= {1986},
  pages		= {192--220},
  issn		= {0075-4102},
  coden		= {JRMAA8}
}

@Article{	  atkin-lehner,
  author	= {Atkin, A.\thinspace{}O.\thinspace{}L. and Lehner, J.},
  title		= {Hecke operators on \protect{$\Gamma \sb{0}(m)$}},
  journal	= {Math. Ann.},
  volume	= {185},
  year		= {1970},
  pages		= {134--160}
}

@article {bdsbt,
    AUTHOR = {Buzzard, Kevin and Dickinson, Mark and Shepherd-Barron, Nick
              and Taylor, Richard},
     TITLE = {On icosahedral {A}rtin representations},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {109},
      YEAR = {2001},
    NUMBER = {2},
     PAGES = {283--318},
      ISSN = {0012-7094},
     CODEN = {DUMJAO},
   MRCLASS = {11F80 (11F33 11G18 11R42)},
  MRNUMBER = {MR1845181 (2002k:11078)},
MRREVIEWER = {Gebhard B{\"o}ckle},
}

@Book{		  bgr,
  author	= {Bosch, S. and G{\"u}ntzer, U. and Remmert, R.},
  title		= {Non-{A}rchimedean analysis: A systematic approach to rigid
		  analytic geometry},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1984},
  pages		= {xii+436},
  isbn		= {3-540-12546-9},
  mrclass	= {32K10 (30G05 46P05)},
  mrnumber	= {86b:32031},
  mrrevr	= {W. Bartenwerfer}
}

@InCollection{	  birch:atkin,
  author	= {Birch, B.},
  title		= {Atkin and the {A}tlas {L}ab},
  booktitle	= {Proceedings of the conference in honor of
		  A.\thinspace{}O.\thinspace{}L. Atkin held at the University
		  of Illinois, Chicago, IL, September 1995},
  pages		= {13--20},
  publisher	= {Amer. Math. Soc.},
  address	= {Providence, RI},
  year		= {1998},
  mrclass	= {11-03 (01A60 11F30 11F33)},
  mrnumber	= {99c:11002},
  mrrevr	= {V. Kumar Murty}
}


@InCollection{	  birch:bsd,
  author	= {Birch, B.\thinspace{}J.},
  title		= {Elliptic curves over \protect{${\mathbf{Q}}$: {A}}
		  progress report},
  booktitle	= {1969 Number Theory Institute (Proc. Sympos. Pure Math.,
		  Vol. XX, State Univ. New York, Stony Brook, N.Y., 1969)},
  pages		= {396--400},
  publisher	= {Amer. Math. Soc.},
  address	= {Providence, R.I.},
  year		= {1971}
}

@InCollection{	  birch:cyclo,
  author	= {Birch, B.\thinspace{}J.},
  title		= {Cyclotomic fields and {K}ummer extensions},
  booktitle	= {Algebraic Number Theory (Proc. Instructional Conf.,
		  Brighton, 1965)},
  pages		= {85--93},
  publisher	= {Thompson, Washington, D.C.},
  year		= {1967}
}

@InCollection{	  birch:edsac,
  author	= {Birch, B. J.},
  title		= {Conjectures concerning elliptic curves},
  booktitle	= {Proceedings of Symposia in Pure Mathematics, VIII},
  pages		= {106--112},
  publisher	= {Amer. Math. Soc.},
  address	= {Providence, R.I.},
  year		= {1965},
  mrclass	= {14.49 (14.40)},
  mrnumber	= {30 \#4759},
  mrreviewer	= {J. W. S. Cassels}
}

@InCollection{	  birch:hecke_actions,
  author	= {Birch, B. J.},
  title		= {Hecke actions on classes of ternary quadratic forms},
  booktitle	= {Computational number theory (Debrecen, 1989)},
  pages		= {191--212},
  publisher	= {de Gruyter},
  address	= {Berlin},
  year		= {1991},
  mrclass	= {11E45 (11E20 11F11 11G05 11Y35)},
  mrnumber	= {93i:11047},
  mrrevr	= {Rainer Schulze-Pillot}
}

@InCollection{	  bloch-kato,
  author	= {Bloch, S. and Kato, K.},
  title		= {\protect{${L}$}-functions and \protect{T}amagawa numbers
		  of motives},
  booktitle	= {The Grothendieck Festschrift, Vol. \protect{I}},
  pages		= {333--400},
  publisher	= {Birkh\"auser Boston},
  address	= {Boston, MA},
  year		= {1990}
}

@Article{	  bockle:density,
  author	= {B{\"o}ckle, Gebhard},
  title		= {On the density of modular points in universal deformation
		  spaces},
  journal	= {Amer. J. Math.},
  fjournal	= {American Journal of Mathematics},
  volume	= {123},
  year		= {2001},
  number	= {5},
  pages		= {985--1007},
  issn		= {0002-9327},
  coden		= {AJMAAN},
  mrclass	= {11F80},
  mrnumber	= {1 854 117}
}

@Article{	  bolling:sha,
  author	= {B{\"o}lling, Reinhard},
  title		= {Die {O}rdnung der {S}chafarewitsch-{T}ate-{G}ruppe kann
		  beliebig gro\ss \ werden},
  journal	= {Math. Nachr.},
  volume	= {67},
  year		= {1975},
  pages		= {157--179},
  mrclass	= {14K15},
  mrnumber	= {52 \#5684},
  mrreviewer	= {J. W. S. Cassels}
}

@Proceedings{	  boston,
  title		= {Modular forms and \protect{F}ermat's last theorem
		  (Boston,MA, 1995)},
  editor	= {Cornell, G. and Silverman, J.\thinspace{}H. and Stevens,
		  G.},
  note		= {Papers from the Instructional Conference on Number Theory
		  and Arithmetic Geometry held at Boston University, Boston,
		  MA, August 9--18, 1995},
  publisher	= {Springer-Verlag},
  address	= {New York},
  year		= {1997},
  pages		= {xx+582},
  isbn		= {0-387-94609-8}
}

@Article{	  boston-lenstra-ribet,
  author	= {N. Boston and \protect{H.\thinspace{}W. Lenstra, Jr.} and
		  K.\thinspace{}A. Ribet},
  title		= {Quotients of group rings arising from two-dimensional
		  representations},
  journal	= {C. R. Acad. Sci. Paris S\'er. I Math.},
  fjournal	= {Comptes Rendus de l'Acad\'emie des Sciences. S\'erie I.
		  Math\'ematique},
  volume	= {312},
  year		= {1991},
  number	= {4},
  pages		= {323--328},
  issn		= {0764-4442},
  coden		= {CASMEI}
}

@Article{	  breuil-conrad-diamond-taylor,
  author	= {Breuil, C. and Conrad, B. and Diamond, F. and Taylor, R.},
  title		= {On the modularity of elliptic curves over {$\mathbf{Q}$}:
		  wild 3-adic exercises},
  journal	= {J. Amer. Math. Soc.},
  fjournal	= {Journal of the American Mathematical Society},
  volume	= {14},
  year		= {2001},
  number	= {4},
  pages		= {843--939 (electronic)},
  issn		= {0894-0347},
  mrclass	= {11G05 (11F80 11G07 14G35)},
  mrnumber	= {2002d:11058},
  mrreviewer	= {Karl Rubin}
}

@Article{	  brue,
  author	= {Brueggeman, S.},
  title		= {The non-existence of certain \protect{Galois} extensions
		  unramified outside 5},
  journal	= {Journal of Number Theory},
  volume	= {75},
  year		= {1999},
  pages		= {47--52}
}

@Article{	  brumer-mcguinness,
  author	= {Brumer, A. and McGuinness, O.},
  title		= {The behavior of the {M}ordell-{W}eil group of elliptic
		  curves},
  journal	= {Bull. Amer. Math. Soc. (N.S.)},
  fjournal	= {American Mathematical Society. Bulletin. New Series},
  volume	= {23},
  year		= {1990},
  number	= {2},
  pages		= {375--382},
  issn		= {0273-0979},
  coden		= {BAMOAD},
  note		= {Data at \protect{\tt http://oisinmc.com/math/310716/}}
}

@Article{	  brumer:rank,
  author	= {Brumer, A.},
  title		= {The rank of \protect{${J}\sb 0({N})$}},
  note		= {Columbia University Number Theory Seminar (New York,
		  1992)},
  journal	= {Ast\'erisque},
  fjournal	= {Ast\'erisque},
  number	= {228},
  year		= {1995},
  pages		= {3, 41--68},
  issn		= {0303-1179}
}

@Article{	  buhler-gross,
  author	= {Buhler, J.\thinspace{}P. and Gross, B.\thinspace{}H.},
  title		= {Arithmetic on elliptic curves with complex multiplication.
		  {I}{I}},
  journal	= {Invent. Math.},
  fjournal	= {Inventiones Mathematicae},
  volume	= {79},
  year		= {1985},
  number	= {1},
  pages		= {11--29},
  issn		= {0020-9910},
  coden		= {INVMBH},
  mrclass	= {11G40 (11G05 14K22)},
  mrnumber	= {86j:11066},
  mrreviewer	= {Kenneth Kramer}
}

@Book{		  buhler:thesis,
  author	= {Buhler, J.\thinspace{}P.},
  title		= {Icosahedral \protect{G}alois representations},
  note		= {Lecture Notes in Mathematics, Vol. 654},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1978},
  pages		= {ii+143},
  isbn		= {3-540-08844-X}
}

@article {bump-friedberg-hoffstein:nonvanishing,
    AUTHOR = {Bump, Daniel and Friedberg, Solomon and Hoffstein, Jeffrey},
     TITLE = {Nonvanishing theorems for {$L$}-functions of modular forms and
              their derivatives},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {102},
      YEAR = {1990},
    NUMBER = {3},
     PAGES = {543--618},
      ISSN = {0020-9910},
     CODEN = {INVMBH},
   MRCLASS = {11F66 (11F67 11G05 11G40)},
  MRNUMBER = {MR1074487 (92a:11058)},
MRREVIEWER = {Alexey A. Panchishkin},
}

@Article{	  bump-friedberg-hoffstein,
  author	= {Bump, D. and Friedberg, S. and Hoffstein, J.},
  title		= {Eisenstein series on the metaplectic group and
		  nonvanishing theorems for automorphic
		  \protect{${L}$}-functions and their derivatives},
  journal	= {Ann. of Math. (2)},
  fjournal	= {Annals of Mathematics. Second Series},
  volume	= {131},
  year		= {1990},
  number	= {1},
  pages		= {53--127},
  issn		= {0003-486X},
  coden		= {ANMAAH}
}

@Article{	  buzzard-stein:artin,
  author	= {Buzzard, K. and Stein, W.\thinspace{}A.},
  title		= {A mod five approach to modularity of icosahedral {G}alois
		  representations},
  journal	= {Pacific J. Math.},
  fjournal	= {Pacific Journal of Mathematics},
  volume	= {203},
  year		= {2002},
  number	= {2},
  pages		= {265--282},
  issn		= {0030-8730},
  coden		= {PJMAAI},
  mrclass	= {11F80},
  mrnumber	= {2003c:11052},
  mrreviewer	= {Mark Edward Tristan Dickinson}
}

@Article{	  buzzard-taylor,
  author	= {Buzzard, K. and Taylor, R.},
  title		= {Companion forms and weight one forms},
  journal	= {Ann. of Math. (2)},
  fjournal	= {Annals of Mathematics. Second Series},
  volume	= {149},
  year		= {1999},
  number	= {3},
  pages		= {905--919},
  issn		= {0003-486X},
  coden		= {ANMAAH},
  mrclass	= {11Fxx},
  mrnumber	= {1 709 306}
}

@Article{	  buzzard:level,
  author	= {Buzzard, K.},
  title		= {On level-lowering for mod 2 representations},
  journal	= {preprint}
}

@Article{	  buzzard:t2,
  author	= {Buzzard, Kevin},
  title		= {On the eigenvalues of the {H}ecke operator {$T\sb 2$}},
  journal	= {J. Number Theory},
  fjournal	= {Journal of Number Theory},
  volume	= {57},
  year		= {1996},
  number	= {1},
  pages		= {130--132},
  issn		= {0022-314X},
  coden		= {JNUTA9},
  mrclass	= {11F25},
  mrnumber	= {96m:11033},
  mrreviewer	= {Thomas R. Shemanske}
}

@Article{	  carayol:modell,
  author	= {Carayol, H.},
  title		= {Sur les \protect{repr\'esentations} galoisiennes modulo
		  \protect{$\ell$ attach\'ees} aux formes modulaires},
  journal	= {Duke Math. J.},
  volume	= {59},
  year		= {1989},
  pages		= {785--801}
}

@Article{	  carearly,
  author	= "Carayol, H.",
  title		= {Sur les \protect{repr\'esentations}
		  \protect{$\ell$-adiques} \protect{associ\'ees} aux formes
		  modulaires de \protect{Hilbert}},
  journal	= {Ann. scient. \protect{\'Ec.} Norm. Sup., \protect{$4^{\rm
		  eb}$ s\'erie}},
  volume	= {19},
  year		= {1986},
  pages		= {409--468}
}

@InProceedings{	  casselman,
  author	= {Casselman, W.},
  title		= {On representations of \protect{${\rm {G}{L}}\sb{2}$} and
		  the arithmetic of modular curves},
  booktitle	= {Modular functions of one variable, II (Proc. Internat.
		  Summer School, Univ. Antwerp, Antwerp, 1972)},
  pages		= {107--141. Lecture Notes in Math., Vol. 349},
  publisher	= {Springer},
  address	= {Berlin},
  year		= {1973}
}

@Book{		  cassels-flynn,
  author	= {Cassels, J.\thinspace{}W.\thinspace{}S. and Flynn,
		  E.\thinspace{}V.},
  title		= {Prolegomena to a middlebrow arithmetic of curves of genus
		  \protect{$2$}},
  publisher	= {Cambridge University Press},
  address	= {Cambridge},
  year		= {1996},
  pages		= {xiv+219},
  isbn		= {0-521-48370-0},
  mrclass	= {11G30 (11Y50 14G25)},
  mrnumber	= {97i:11071},
  mrrevr	= {Joseph H. Silverman}
}

@Proceedings{	  cassels-frohlich,
  title		= {Algebraic number theory},
  booktitle	= {Proceedings of the instructional conference held at the
		  University of Sussex, Brighton, September 1--17, 1965},
  editor	= {Cassels, J.\thinspace{}W.\thinspace{}S. and
		  \protect{Fr{\"o}hlich}, A.},
  note		= {Reprint of the 1967 original},
  publisher	= {Academic Press Inc. [Harcourt Brace Jovanovich
		  Publishers]},
  address	= {London},
  year		= {1986},
  pages		= {xviii+366},
  isbn		= {0-12-163251-2}
}

@Article{	  cassels:arithmeticiii,
  author	= {Cassels, J.\thinspace{}W.\thinspace{}S.},
  title		= {{A}rithmetic on curves of genus $1$. {I}{I}{I}. {T}he
		  {T}ate-\v {S}afarevi\v c and {S}elmer groups},
  journal	= {Proc. London Math. Soc. (3)},
  volume	= {12},
  year		= {1962},
  pages		= {259--296},
  mrclass	= {14.49},
  mrnumber	= {29 \#1212}
}

@Article{	  cassels:arithmeticiv,
  author	= {Cassels, J.\thinspace{}W.\thinspace{}S.},
  title		= {Arithmetic on curves of genus \protect{$1$}. {I}{V}.
		  {P}roof of the {H}auptvermutung},
  journal	= {J. Reine Angew. Math.},
  volume	= {211},
  year		= {1962},
  pages		= {95--112}
}

@Article{	  cassels:arithmeticv,
  author	= {Cassels, J.\thinspace{}W.\thinspace{}S.},
  title		= {Arithmetic on curves of genus 1. {V}. {T}wo
		  counterexamples},
  journal	= {J. London Math. Soc.},
  volume	= {38},
  year		= {1963},
  pages		= {244--248}
}

@Article{	  cassels:bigsha,
  author	= {Cassels, J.\thinspace{}W.\thinspace{}S.},
  title		= {Arithmetic on curves of genus $1$. {V}{I}. {T}he {T}ate-\v
		  {S}afarevi\v c group can be arbitrarily large},
  journal	= {J. Reine Angew. Math.},
  volume	= {214/215},
  year		= {1964},
  pages		= {65--70},
  mrclass	= {14.49 (10.12)},
  mrnumber	= {29 \#104},
  mrreviewer	= {P. Abellanas}
}

@Article{	  cassels:diophantinecurve,
  author	= {Cassels, J.\thinspace{}W.\thinspace{}S.},
  title		= {Diophantine equations with special reference to elliptic
		  curves},
  journal	= {J. London Math. Soc.},
  volume	= {41},
  year		= {1966},
  pages		= {193--291}
}

@InCollection{	  cassels:global,
  author	= {Cassels, J.\thinspace{}W.\thinspace{}S.},
  title		= {Global fields},
  booktitle	= {Algebraic Number Theory (Proc. Instructional Conf.,
		  Brighton, 1965)},
  pages		= {42--84},
  publisher	= {Thompson, Washington, D.C.},
  year		= {1967}
}

@Article{	  cerednik,
  author	= {{\v{C}}erednik, I.\thinspace{}V.},
  title		= {Uniformization of algebraic curves by discrete arithmetic
		  subgroups of \protect{${\rm {P}{G}{L}}\sb{2}(k\sb{w})$}
		  with compact quotient spaces},
  journal	= {Mat. Sb. (N.S.)},
  volume	= {100(142)},
  year		= {1976},
  number	= {1},
  pages		= {59--88, 165}
}

@Article{	  cheryl,
  author	= {Beaver, Cheryl DeLorme},
  title		= {$5$-torsion in the {S}hafarevich-{T}ate group of a family
		  of elliptic curves},
  journal	= {J. Number Theory},
  fjournal	= {Journal of Number Theory},
  volume	= {82},
  year		= {2000},
  number	= {1},
  pages		= {25--46},
  issn		= {0022-314X},
  coden		= {JNUTA9},
  mrclass	= {11G05 (11G07)},
  mrnumber	= {2001d:11059},
  mrreviewer	= {Kenneth Kramer}
}

@Article{	  chevalley:thm,
  author	= {Chevalley, C.},
  title		= {Une d\'emonstration d'un th\'eor\`eme sur les groupes
		  alg\'ebriques},
  journal	= {J. Math. Pures Appl. (9)},
  volume	= {39},
  year		= {1960},
  pages		= {307--317},
  mrclass	= {14.50},
  mrnumber	= {23 \#A3743},
  mrreviewer	= {I. Barsotti}
}

@Book{		  cime-1997,
  author	= "Viola, C.",
  title		= "{Arithmetic theory of elliptic curves. Lectures given at
		  the 3rd session of the {C}entro {I}nternazionale
		  {M}atematico {E}stivo \protect{(CIME)}.}",
  language	= "English",
  source	= "{{L}ecture {N}otes in {M}athematics. 1716. {B}erlin:
		  {S}pringer. viii, 260 p. DM 74.00; oeS 541.00; sFr. 67.50;
		  \sterling 28.50; \$ 52.80 (1999). [ISBN 3-540-66546-3/hbk;
		  ISSN 0075-8434]}",
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1997},
  pages		= {260}
}

@Article{	  cmi:problems,
  author	= {Clay Mathematics Institute},
  title		= {Millennium Prize Problems,\hfill\\{\tt
		  http://www.claymath.org/Millennium\_Prize\_Problems/}}
}

@Article{	  coates-wiles:bsd,
  author	= {Coates, J. and Wiles, A.},
  title		= {On the conjecture of {B}irch and {S}winnerton-{D}yer},
  journal	= {Invent. Math.},
  volume	= {39},
  year		= {1977},
  number	= {3},
  pages		= {223--251},
  mrclass	= {14G10 (10D15 14G25)},
  mrnumber	= {57 \#3134},
  mrreviewer	= {Kenneth A. Ribet}
}

@Article{	  cohen-oesterle:dimensions,
  author	= {Cohen, H. and Oesterl{\'e}, J.},
  title		= {Dimensions des espaces de formes modulaires},
  booktitle	= {Modular functions of one variable, VI (Proc. Second
		  Internat. Conf., Univ. Bonn, Bonn, 1976)},
  pages		= {69--78. Lecture Notes in Math., Vol. 627},
  publisher	= {Springer},
  address	= {Berlin},
  year		= {1977},
  mrclass	= {10D15},
  mrnumber	= {57 \#12396},
  mrrevr	= {R. A. Rankin}
}

@Book{		  cohen:course_ant,
  author	= {Cohen, H.},
  title		= {A course in computational algebraic number theory},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1993},
  pages		= {xii+534},
  isbn		= {3-540-55640-0},
  mrclass	= {11Y40 (11Rxx 68Q40)},
  mrnumber	= {94i:11105},
  mrreviewer	= {Joe P. Buhler}
}

@Article{	  coleman-edixhoven,
  author	= {Coleman, R.\thinspace{}F. and Edixhoven, B.},
  title		= {On the semi-simplicity of the \protect{${U}\sb
		  p$}-operator on modular forms},
  journal	= {Math. Ann.},
  fjournal	= {Mathematische Annalen},
  volume	= {310},
  year		= {1998},
  number	= {1},
  pages		= {119--127},
  issn		= {0025-5831},
  coden		= {MAANA},
  mrclass	= {11F25 (11F11 11F33 11F85)},
  mrnumber	= {99b:11043},
  mrrevr	= {Alexey A. Panchishkin}
}


@Article{	  coleman-voloch,
  author	= {Coleman, R.\thinspace{}F. and Voloch, J.\thinspace{}F.},
  title		= {Companion forms and \protect{K}odaira-\protect{S}pencer
		  theory},
  journal	= {Invent. Math.},
  fjournal	= {Inventiones Mathematicae},
  volume	= {110},
  year		= {1992},
  number	= {2},
  pages		= {263--281},
  issn		= {0020-9910},
  coden		= {INVMBH}
}

@Article{	  coleman:banach,
  author	= {Coleman, R.\thinspace{}F.},
  title		= {$p$-adic {B}anach spaces and families of modular forms},
  journal	= {Invent. Math.},
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  mrnumber	= {98b:11047},
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}

@Article{	  coleman:classical,
  author	= {Coleman, R.\thinspace{}F.},
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  mrnumber	= {97d:11090a},
  mrrevr	= {Fernando Q. Gouv\^ea}
}

@Article{	  coleman:classical_higher,
  author	= {Coleman, R.\thinspace{}F.},
  title		= {Classical and overconvergent modular forms of higher
		  level},
  journal	= {J. Th\'eor. Nombres Bordeaux},
  fjournal	= {Journal de Th\'eorie des Nombres de Bordeaux},
  volume	= {9},
  year		= {1997},
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  pages		= {395--403},
  issn		= {1246-7405},
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  mrnumber	= {99g:11071},
  mrrevr	= {Conjeeveram S. Rajan}
}

@Article{	  coleman:monodromy,
  author	= {Coleman, R.},
  title		= {The {M}onodromy {P}airing},
  journal	= {Asian Math. Journal},
  volume	= {4},
  year		= {2000},
  pages		= {315--330}
}

@Article{	  coleman:serre,
  author	= {Coleman, R.\thinspace{}F.},
  title		= {Serre's conjecture: {T}he {J}ugentraum of the 20th
		  century},
  note		= {XII School of Algebra, Part I (Portuguese) (Diamantina,
		  1992)},
  journal	= {Mat. Contemp.},
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  volume	= {6},
  year		= {1994},
  pages		= {13--18},
  issn		= {0103-9059},
  mrclass	= {12F05 (11F03 12F12)},
  mrnumber	= {95j:12003},
  mrrevr	= {Henri Darmon}
}

@Article{	  colmez_fontaine,
  author	= {Colmez, P. and Fontaine, J.-M.},
  title		= {Construction des repr\'esentations {$p$}-adiques
		  semi-stables},
  journal	= {Invent. Math.},
  fjournal	= {Inventiones Mathematicae},
  volume	= {140},
  year		= {2000},
  number	= {1},
  pages		= {1--43},
  issn		= {0020-9910},
  coden		= {INVMBH},
  mrclass	= {11S23 (14F30 14F40)},
  mrnumber	= {2001g:11184},
  mrreviewer	= {Mark Kisin}
}

@Article{	  conrad-diamond-taylor:modularity,
  author	= {Conrad, B. and Diamond, F. and Taylor, R.},
  title		= {Modularity of certain potentially
		  \protect{B}arsotti-\protect{T}ate \protect{G}alois
		  representations},
  journal	= {J. Amer. Math. Soc.},
  fjournal	= {Journal of the American Mathematical Society},
  volume	= {12},
  year		= {1999},
  number	= {2},
  pages		= {521--567},
  issn		= {0894-0347}
}

@Article{	  conrad-edixhoven-stein:j1p,
  author	= {Conrad, B. and Edixhoven, S. and Stein, W.\thinspace{}A.},
  title		= {${J}_1(p)$ {H}as {C}onnected {F}ibers},
  year		= 2003,
  journal	= {Documenta Mathematica},
  volume	= {8},
  pages		= {331--408}
}

@Article{	  conrad-stein:compgroup,
  author	= {Conrad, B. and Stein, W.\thinspace{}A.},
  title		= {Component groups of purely toric quotients},
  journal	= {Math. Res. Lett.},
  fjournal	= {Mathematical Research Letters},
  volume	= {8},
  year		= {2001},
  number	= {5-6},
  pages		= {745--766},
  issn		= {1073-2780},
  mrclass	= {11G18 (11G10 11G40 14K15)},
  mrnumber	= {2003f:11087},
  mrreviewer	= {Antoine Chambert-Loir}
}

@Article{	  conrad:eulerprod,
  author	= {Conrad, K.},
  title		= {{P}artial {E}uler products on the critical line},
  journal	= {Preprint},
  year		= {2003}
}

@InCollection{	  conrad:shimura,
  author	= {Conrad, B.},
  title		= {The Shimura Construction in Weight 2 (appendix to
		  {R}ibet-{S}tein, {L}ectures on {S}erre's {C}onjecture)},
  booktitle	= {Arithmetic algebraic geometry (Park City, UT, 1999)},
  series	= {IAS/Park City Math. Ser.},
  volume	= {9},
  pages		= {205--232},
  publisher	= {Amer. Math. Soc.},
  address	= {Providence, RI},
  year		= {2001},
  mrclass	= {11F80 (11F66 11G05)},
  mrnumber	= {2002h:11047}
}

@InCollection{	  conrey-farmer:nonvanish,
  author	= {Conrey, J.\thinspace{}B. and Farmer, D.\thinspace{}W.},
  title		= {Hecke operators and the nonvanishing of {$L$}-functions},
  booktitle	= {Topics in number theory (University Park, PA, 1997)},
  series	= {Math. Appl.},
  volume	= {467},
  pages		= {143--150},
  publisher	= {Kluwer Acad. Publ.},
  address	= {Dordrecht},
  year		= {1999},
  mrclass	= {11F67 (11F25)},
  mrnumber	= {2000f:11055},
  mrreviewer	= {Vinayak Vatsal}
}

@Article{	  cremona-luiz,
  title		= {\protect{C++} matrix classes},
  author	= {Cremona, J.\thinspace{}E. and Luiz F.}
}

@Article{	  cremona-mazur,
  author	= {Cremona, J.\thinspace{}E. and Mazur, B.},
  title		= {Visualizing elements in the {S}hafarevich-{T}ate group},
  journal	= {Experiment. Math.},
  fjournal	= {Experimental Mathematics},
  volume	= {9},
  year		= {2000},
  number	= {1},
  pages		= {13--28},
  issn		= {1058-6458},
  mrclass	= {11Gxx (14Gxx)},
  mrnumber	= {1 758 797}
}

@Book{		  cremona:algs,
  author	= {Cremona, J.\thinspace{}E.},
  title		= {Algorithms for modular elliptic curves},
  edition	= {Second},
  publisher	= {Cambridge University Press},
  address	= {Cambridge},
  year		= {1997},
  pages		= {vi+376},
  isbn		= {0-521-59820-6},
  note		= {\mbox{}\\{\tt
		  http://www.maths.nott.ac.uk/personal/jec/book/}}
}

@Article{	  cremona:gammaone,
  author	= {Cremona, J.\thinspace{}E.},
  title		= {Modular symbols for \protect{$\Gamma\sb 1({N})$} and
		  elliptic curves with everywhere good reduction},
  journal	= {Math. Proc. Cambridge Philos. Soc.},
  fjournal	= {Mathematical Proceedings of the Cambridge Philosophical
		  Society},
  volume	= {111},
  year		= {1992},
  number	= {2},
  pages		= {199--218},
  issn		= {0305-0041},
  coden		= {MPCPCO}
}

@article{	  cremona:onlinetables,
  author	= {Cremona, J.\thinspace{}E.},
  title		= {{E}lliptic {C}urves {D}ata},
  note = {\url{http://www.warwick.ac.uk/~masgaj/ftp/data/}}
}

@Article{	  cremona:periods,
  author	= {Cremona, J.\thinspace{}E.},
  title		= {Computing periods of cusp forms and modular elliptic
		  curves},
  journal	= {Experiment. Math.},
  fjournal	= {Experimental Mathematics},
  volume	= {6},
  year		= {1997},
  number	= {2},
  pages		= {97--107},
  issn		= {1058-6458}
}

@Book{		  curtis-reiner,
  author	= {Curtis, C.\thinspace{}W. and Reiner, I.},
  title		= {Representation theory of finite groups and associative
		  algebras},
  note		= {Pure and Applied Mathematics, Vol. XI},
  publisher	= {Interscience Publishers, a division of John Wiley \& Sons,
		  New York-London},
  year		= {1962},
  pages		= {xiv+685}
}

@InCollection{	  darmon-bsd,
  author	= {Darmon, H.},
  title		= {Wiles' theorem and the arithmetic of elliptic curves},
  booktitle	= {Modular forms and Fermat's last theorem (Boston, MA,
		  1995)},
  pages		= {549--569},
  publisher	= {Springer},
  address	= {New York},
  year		= {1997},
  mrclass	= {11G40 (11G05)},
  mrnumber	= {1 638 495}
}

@Article{	  darmon-merel,
  author	= {Darmon, H. and Merel, L.},
  title		= {Winding quotients and some variants of {F}ermat's last
		  theorem},
  journal	= {J. Reine Angew. Math.},
  fjournal	= {Journal f\"ur die Reine und Angewandte Mathematik},
  volume	= {490},
  year		= {1997},
  pages		= {81--100},
  issn		= {0075-4102},
  coden		= {JRMAA8},
  mrclass	= {11G18 (11D41 11F80 11G05)},
  mrnumber	= {98h:11076},
  mrrevr	= {Kenneth Kramer}
}

@InCollection{	  darmon:serre,
  author	= {Darmon, Henri},
  title		= {Serre's conjectures},
  booktitle	= {Seminar on Fermat's Last Theorem (Toronto, ON,
		  1993--1994)},
  pages		= {135--153},
  publisher	= {Amer. Math. Soc.},
  address	= {Providence, RI},
  year		= {1995},
  mrclass	= {11F80 (11F11 11R32)},
  mrnumber	= {96h:11048},
  mrrevr	= {Dipendra Prasad}
}

@InCollection{	  ddt,
  author	= {Darmon, H. and Diamond, F. and Taylor, R.},
  title		= {Fermat's last theorem},
  booktitle	= {Current developments in mathematics, 1995 (Cambridge,
		  MA)},
  pages		= {1--154},
  publisher	= {Internat. Press},
  address	= {Cambridge, MA},
  year		= {1994}
}

@InProceedings{	  deligne,
  author	= {Deligne, P.},
  title		= {Formes modulaires et \protect{repr\'{e}sentations
		  $\ell$-adiques.}},
  note		= {Lecture Notes in Mathematics, Vol. 179},
  publisher	= {Springer-Verlag},
  booktitle	= {\protect{S\'{e}m.} Bourbaki no. 355, 1968/69},
  address	= {Berlin and New York},
  year		= {1971},
  pages		= {139--172}
}

@InProceedings{	  deligne-rapoport,
  author	= {Deligne, P. and Rapoport, M.},
  title		= {Les sch\'emas de modules de courbes elliptiques},
  booktitle	= {Modular functions of one variable, II (Proc. Internat.
		  Summer School, Univ. Antwerp, Antwerp, 1972)},
  pages		= {143--316. Lecture Notes in Math., Vol. 349},
  publisher	= {Springer},
  address	= {Berlin},
  year		= {1973}
}

@Article{	  deligne-serre,
  author	= {Deligne, P. and Serre, J-P.},
  title		= {Formes modulaires de poids $1$},
  journal	= {Ann. Sci. \'Ecole Norm. Sup. (4)},
  volume	= {7},
  year		= {1974},
  pages		= {507--530 (1975)}
}

@InCollection{	  diamond-im,
  author	= {Diamond, F. and Im, J.},
  title		= {Modular forms and modular curves},
  booktitle	= {Seminar on {F}ermat's {L}ast {T}heorem},
  pages		= {39--133},
  pppublisher	= {Amer. Math. Soc.},
  address	= {Providence, RI},
  year		= {1995}
}

@Article{	  diamond-kramer,
  author	= {Diamond, F. and Kramer, K.},
  title		= {Modularity of a family of elliptic curves},
  journal	= {Math. Res. Lett.},
  fjournal	= {Mathematical Research Letters},
  volume	= {2},
  year		= {1995},
  number	= {3},
  pages		= {299--304},
  issn		= {1073-2780}
}

@InProceedings{	  diamond:refined,
  author	= {Diamond, F.},
  title		= {The refined conjecture of \protect{S}erre},
  booktitle	= {Elliptic curves, modular forms, \& \protect{F}ermat's last
		  theorem (\protect{H}ong \protect{K}ong, 1993)},
  pages		= {22--37},
  publisher	= {Internat. Press},
  address	= {Cambridge, MA},
  year		= {1995}
}

@Article{	  dickinson:thesis,
  author	= {Dickinson, M.},
  title		= {On the modularity of certain $2$-adic Galois
		  representations},
  journal	= {Harvard Ph.D. thesis},
  year		= {2000}
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@Book{		  dixcohomologie,
  title		= {Dix expos\'es sur la cohomologie des sch\'emas},
  note		= {Advanced Studies in Pure Mathematics, Vol. 3},
  publisher	= {North-Holland Publishing Co.},
  address	= {Amsterdam},
  year		= {1968},
  pages		= {vi+386},
  mrclass	= {14.55},
  mrnumber	= {39 #2777}
}

@Article{	  doud,
  author	= {Doud, D.},
  title		= {\protect{${S}\sb 4$} and \protect{$\tilde {S}{}\sb 4$}
		  extensions of \protect{${\bf {Q}}$} ramified at only one prime},
  journal	= {J. Number Theory},
  fjournal	= {Journal of Number Theory},
  volume	= {75},
  year		= {1999},
  number	= {2},
  pages		= {185--197},
  issn		= {0022-314X},
  coden		= {JNUTA9}
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@Article{	  drinfeld:coverings,
  author	= {Drinfeld, V.\thinspace{}G.},
  title		= {Coverings of \protect{$p$-adic} symmetric domains},
  journal	= {Funkcional. Anal. i Prilov zen.},
  volume	= {10},
  year		= {1976},
  number	= {2},
  pages		= {29--40}
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@Article{	  dummigan-stein-watkins:motives,
  author	= {Dummigan, N. and Watkins, M. and Stein, W.\thinspace{}A.},
  title		= {{Constructing Elements in Shafarevich-Tate Groups of
		  Modular Motives}},
  journal	= {Number theory and algebraic geometry, ed. by Miles Reid
		  and Alexei Skorobogatov},
  year		= {2003},
  volume	= {303},
  series	= {Lecture Notes Series},
  publisher	= {Cambridge Univ. Press},
  pages		= {91--118}
}

@Article{	  dummigan:cp,
    AUTHOR = {Dummigan, N.},
     TITLE = {Period ratios of modular forms},
   JOURNAL = {Math. Ann.},
  FJOURNAL = {Mathematische Annalen},
    VOLUME = {318},
      YEAR = {2000},
    NUMBER = {3},
     PAGES = {621--636},
      ISSN = {0025-5831},
     CODEN = {MAANA},
   MRCLASS = {11F67 (11F33 11G40)},
  MRNUMBER = {MR1800772 (2002a:11049)},
MRREVIEWER = {Kevin L. James},
}

 
@article {dummigan:congruences,
    AUTHOR = {Dummigan, N.},
     TITLE = {Congruences of modular forms and {S}elmer groups},
   JOURNAL = {Math. Res. Lett.},
  FJOURNAL = {Mathematical Research Letters},
    VOLUME = {8},
      YEAR = {2001},
    NUMBER = {4},
     PAGES = {479--494},
      ISSN = {1073-2780},
   MRCLASS = {11F33 (11F37 11F67 11G40)},
  MRNUMBER = {MR1849264 (2002k:11064)},
MRREVIEWER = {Andrea Mori},
}


@Article{	  edixcole,
  author	= {Coleman, R.\thinspace{}F. and Edixhoven, B.},
  title		= {On the semi-simplicity of the \protect{${U}\sb
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  journal	= {Math. Ann.},
  fjournal	= {Mathematische Annalen},
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  year		= {1998},
  number	= {1},
  pages		= {119--127},
  issn		= {0025-5831},
  coden		= {MAANA}
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@Article{	  edixhoven:comparison,
  author	= {Edixhoven, B.},
  title		= {Comparison of integral structures on spaces of modular
		  forms of weight two, and computation of spaces of forms
		  mod~$2$ of weight one},
  year		= {July, 2003},
  journal	= {preprint}
}

@Article{	  edixhoven:eisen,
  author	= {Edixhoven, B.},
  title		= {L'action de l'alg\`ebre de \protect{H}ecke sur les groupes
		  de composantes des jacobiennes des courbes modulaires est
		  ``\protect{E}isenstein''},
  note		= {Courbes modulaires et courbes de Shimura (Orsay,
		  1987/1988)},
  journal	= {Ast\'erisque},
  fjournal	= {Ast\'erisque},
  number	= {196--197},
  year		= {1991},
  pages		= {7--8, 159--170 (1992)},
  issn		= {0303-1179}
}

@Article{	  edixhoven:erratum,
  author	= {Edixhoven, B.},
  title		= {Erratum and addendum: ``{T}he role of {S}erre's conjecture
		  in the proof of {F}ermat's theorem''},
  journal	= {Gaz. Math.},
  fjournal	= {Gazette des Math\'ematiciens},
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  year		= {1996},
  pages		= {19},
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  mrclass	= {11F33 (11D41 11F80 11G05)},
  mrnumber	= {96k:11055b},
  mrrevr	= {Fernando Q. Gouv\^ea}
}

@InCollection{	  edixhoven:manin,
  author	= {Edixhoven, B.},
  title		= {On the {M}anin constants of modular elliptic curves},
  booktitle	= {Arithmetic algebraic geometry (Texel, 1989)},
  pages		= {25--39},
  publisher	= {Birkh\"auser Boston},
  address	= {Boston, MA},
  year		= {1991},
  mrclass	= {11G05 (14G25)},
  mrnumber	= {92a:11066},
  mrreviewer	= {Philippe Satg{\'e}}
}

@Article{	  edixhoven:minimal,
  author	= {Edixhoven, B.},
  title		= {Minimal resolution and stable reduction of
		  \protect{${X}\sb 0({N})$}},
  journal	= {Ann. Inst. Fourier (Grenoble)},
  fjournal	= {Universit\'e de Grenoble. Annales de l'Institut Fourier},
  volume	= {40},
  year		= {1990},
  number	= {1},
  pages		= {31--67},
  issn		= {0373-0956},
  coden		= {AIFUA7},
  mrclass	= {11G18 (14G35)},
  mrnumber	= {92f:11080},
  mrreviewer	= {Autorreferat}
}

@InProceedings{	  edixhoven:serre,
  author	= {Edixhoven, B.},
  title		= {Serre's conjecture},
  booktitle	= {Modular forms and \protect{F}ermat's last theorem (Boston,
		  MA, 1995)},
  pages		= {209--242},
  publisher	= {Springer},
  address	= {New York},
  year		= {1997}
}

@Article{	  edixhoven:serrerole,
  author	= {Edixhoven, B.},
  title		= {Le r\^{o}le de la conjecture de {S}erre dans la
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  journal	= {Gaz. Math.},
  fjournal	= {Gazette des Math\'ematiciens},
  number	= {66},
  year		= {1995},
  pages		= {25--41},
  issn		= {0224-8999},
  mrclass	= {11F33 (11D41 11F80 11G05)},
  mrnumber	= {96k:11055a},
  mrrevr	= {Fernando Q. Gouv\^ea}
}

@Article{	  edixhoven:tame,
  author	= {Edixhoven, B.},
  title		= {N\'eron models and tame ramification},
  journal	= {Compositio Math.},
  fjournal	= {Compositio Mathematica},
  volume	= {81},
  year		= {1992},
  number	= {3},
  pages		= {291--306},
  issn		= {0010-437X},
  coden		= {CMPMAF},
  mrclass	= {14K15 (11G10)},
  mrnumber	= {93a:14041},
  mrreviewer	= {Min Ho Lee}
}

@Article{	  edixhoven:weight,
  author	= {Edixhoven, B.},
  title		= {The weight in \protect{S}erre's conjectures on modular
		  forms},
  journal	= {Invent. Math.},
  fjournal	= {Inventiones Mathematicae},
  volume	= {109},
  year		= {1992},
  number	= {3},
  pages		= {563--594},
  issn		= {0020-9910},
  coden		= {INVMBH}
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@Article{	  ega4_1,
  author	= {Grothendieck, A.},
  title		= {\'{E}l\'ements de g\'eom\'etrie alg\'ebrique. {I}{V}.
		  \'{E}tude locale des sch\'emas et des morphismes de
		  sch\'emas. {I}},
  journal	= {Inst. Hautes \'Etudes Sci. Publ. Math.},
  number	= {20},
  year		= {1964},
  pages		= {259},
  mrclass	= {14.05 (13.10)},
  mrnumber	= {30 \#3885},
  mrreviewer	= {H. Hironaka}
}

@Article{	  ega4_2,
  author	= {Grothendieck, A.},
  title		= {\'{E}l\'ements de g\'eom\'etrie alg\'ebrique. {I}{V}.
		  \'{E}tude locale des sch\'emas et des morphismes de
		  sch\'emas. {I}{I}},
  journal	= {Inst. Hautes \'Etudes Sci. Publ. Math.},
  number	= {24},
  year		= {1965},
  pages		= {231},
  mrclass	= {14.00},
  mrnumber	= {33 \#7330},
  mrreviewer	= {H. Hironaka}
}

@Article{	  ega4_3,
  author	= {Grothendieck, A.},
  title		= {\'{E}l\'ements de g\'eom\'etrie alg\'ebrique. {I}{V}.
		  \'{E}tude locale des sch\'emas et des morphismes de
		  sch\'emas. {I}{I}{I}},
  journal	= {Inst. Hautes \'Etudes Sci. Publ. Math.},
  number	= {28},
  year		= {1966},
  pages		= {255},
  mrclass	= {14.55},
  mrnumber	= {36 \#178},
  mrreviewer	= {J. P. Murre}
}

@Article{	  ega4_4,
  author	= {Grothendieck, A.},
  title		= {\'{E}l\'ements de g\'eom\'etrie alg\'ebrique. {I}{V}.
		  \'{E}tude locale des sch\'emas et des morphismes de
		  sch\'emas {I}{V}},
  journal	= {Inst. Hautes \'Etudes Sci. Publ. Math.},
  number	= {32},
  year		= {1967},
  pages		= {361},
  mrclass	= {14.55},
  mrnumber	= {39 \#220},
  mrreviewer	= {J. P. Murre}
}

@Article{	  eichler:ideal,
  author	= {Eichler, M.},
  title		= {Uber die Idealklassenzahl total definiter
		  Quaternionenalgebren},
  journal	= {Math. Zeit.},
  volume	= {43},
  year		= {1937},
  pages		= {102--109}
}

@Article{	  eichler:quadratic,
  author	= {Eichler, M.},
  title		= {Quadratische \protect{F}ormen und
		  \protect{M}odulfunktionen},
  journal	= {Acta Arith.},
  volume	= {4},
  year		= {1958},
  pages		= {217--239}
}

@InCollection{	  eigencurve,
  author	= {Coleman, R. and Mazur, B.},
  title		= {The {E}igencurve},
  booktitle	= {Galois representations in arithmetic algebraic geometry
		  (Durham, 1996)},
  pages		= {1--113},
  publisher	= {Cambridge Univ. Press},
  address	= {Cambridge},
  year		= {1998},
  mrclass	= {11Fxx (11Gxx)},
  mrnumber	= {1 696 469}
}

@Book{		  eisenbud,
  author	= {Eisenbud, D.},
  title		= {Commutative Algebra with a View Toward Algebraic
		  Geometry},
  publisher	= {Springer-Verlag},
  address	= {New York},
  year		= {1995},
  pages		= {xvi+785},
  isbn		= {0-387-94268-8; 0-387-94269-6},
  mrclass	= {13-01 (14A05)},
  mrnumber	= {97a:13001},
  mrrevr	= {Matthew Miller}
}

@Book{		  eisenbud-harris,
  author	= {Eisenbud, D. and Harris, J.},
  title		= {{S}chemes, {T}he language of modern algebraic geometry},
  publisher	= {Wadsworth \& Brooks/Cole Advanced Books \& Software},
  address	= {Pacific Grove, CA},
  year		= {1992},
  pages		= {xii+157},
  isbn		= {0-534-17606-2; 0-534-17604-6},
  mrclass	= {14-01 (14A15)},
  mrnumber	= {93k:14001},
  mrrevr	= {Alexey N. Rudakov}
}

@Book{		  eisenbud-harris-2,
  author	= {Eisenbud, D. and Harris, J.},
  title		= {{S}chemes, {T}he language of modern algebraic geometry},
  note		= {Graduate Texts in Mathematics, Vol.\ 197},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {},
  pages		= {}
}

@Book{		  eisenbud_harris:geometry,
  author	= {Eisenbud, D. and Harris, J.},
  title		= {The geometry of schemes},
  publisher	= {Springer-Verlag},
  address	= {New York},
  year		= {2000},
  pages		= {x+294},
  isbn		= {0-387-98638-3; 0-387-98637-5},
  mrclass	= {14A15 (14-01 14C05 14H50 14N05)},
  mrnumber	= {2001d:14002},
  mrreviewer	= {Allen B. Altman}
}

@InCollection{	  elkies:ffield,
  author	= {Elkies, N.\thinspace{}D.},
  title		= {Elliptic and modular curves over finite fields and related
		  computational issues},
  booktitle	= {Computational perspectives on number theory (Chicago, IL,
		  1995)},
  pages		= {21--76},
  publisher	= {Amer. Math. Soc.},
  address	= {Providence, RI},
  year		= {1998}
}

@InCollection{	  elkies:heegner,
  author	= {Elkies, N.\thinspace{}D.},
  title		= {Heegner point computations},
  booktitle	= {Algorithmic number theory (Ithaca, NY, 1994)},
  pages		= {122--133},
  publisher	= {Springer},
  address	= {Berlin},
  year		= {1994}
}

@Article{	  ellenberg-skinner:modularity,
  author	= {Ellenberg, J. and Skinner, C.},
  title		= {On the {M}odularity of {$\Q$}-curves},
  journal	= {{\tt
		  http://www.math.princeton.edu/~ellenber/papers.html\#QCURVE}}
		  ,
  year		= {2000}
}

@Article{	  ellenberg:qcurves_survey,
  author	= {Ellenberg, J.},
  title		= {$\Q$-curves and {G}alois {R}epresentations},
  journal	= {{\tt
		  http://www.math.princeton.edu/~ellenber/papers.html\#MCAV}},
  year		= {2002}
}

@Article{	  emerton:optimal,
    AUTHOR = {Emerton, Matthew},
     TITLE = {Optimal quotients of modular {J}acobians},
   JOURNAL = {Math. Ann.},
  FJOURNAL = {Mathematische Annalen},
    VOLUME = {327},
      YEAR = {2003},
    NUMBER = {3},
     PAGES = {429--458},
      ISSN = {0025-5831},
     CODEN = {MAANA},
   MRCLASS = {11G10 (11F25 11F80 11G18)},
  MRNUMBER = {MR2021024 (2005g:11100)},
MRREVIEWER = {Jacques Tilouine},
}


@Article{	  empirical,
  author	= {Flynn, E.\thinspace{}V. and \protect{Lepr\'{e}vost}, F.
		  and Schaefer, E.\thinspace{}F. and Stein, W.\thinspace{}A.
		  and Stoll, M. and Wetherell, J.\thinspace{}L.},
  title		= {Empirical evidence for the {B}irch and {S}winnerton-{D}yer
		  conjectures for modular {J}acobians of genus 2 curves},
  journal	= {Math. Comp.},
  fjournal	= {Mathematics of Computation},
  volume	= {70},
  year		= {2001},
  number	= {236},
  pages		= {1675--1697 (electronic)},
  issn		= {0025-5718},
  coden		= {MCMPAF},
  mrclass	= {},
  mrnumber	= {1 836 926}
}

@Article{	  faltings-finiteness,
  author	= {Faltings, G.},
  title		= {\protect{Endlichkeitss\"atze f\"ur} abelsche
		  \protect{V}ariet\"aten \"uber \protect{Z}ahlk\"orpern},
  journal	= {Invent. Math.},
  fjournal	= {Inventiones Mathematicae},
  volume	= {73},
  year		= {1983},
  number	= {3},
  pages		= {349--366},
  issn		= {0020-9910},
  coden		= {INVMBH}
}

@Article{	  faltings-jordan,
  author	= {Faltings, G. and Jordan, B.\thinspace{}W.},
  title		= {Crystalline cohomology and \protect{${\rm {G}{L}}(2,{\bf
		  {Q}})$}},
  journal	= {Israel J. Math.},
  fjournal	= {Israel Journal of Mathematics},
  volume	= {90},
  year		= {1995},
  number	= {1-3},
  pages		= {1--66},
  issn		= {0021-2172},
  coden		= {ISJMAP}
}

@InCollection{	  faltings:finiteness,
  author	= {Faltings, G.},
  title		= {Finiteness theorems for abelian varieties over number
		  fields},
  booktitle	= {Arithmetic geometry (Storrs, Conn., 1984)},
  pages		= {9--27},
  note		= {Translated from the German original [Invent.\ Math.\ {\bf
		  73} (1983), no.\ 3, 349--366; ibid.\ {\bf 75} (1984), no.\
		  2, 381; MR 85g:11026ab] by Edward Shipz},
  publisher	= {Springer},
  address	= {New York},
  year		= {1986},
  mrclass	= {11G10 (14K15)},
  mrnumber	= {861 971}
}

@Article{	  farmer-james:maeda,
  author	= {Farmer, D. W. and James, K.},
  title		= {The irreducibility of some level 1 {H}ecke polynomials},
  journal	= {Math. Comp.},
  fjournal	= {Mathematics of Computation},
  volume	= {71},
  year		= {2002},
  number	= {239},
  pages		= {1263--1270 (electronic)},
  issn		= {0025-5718},
  coden		= {MCMPAF},
  mrclass	= {11F25 (11F11)},
  mrnumber	= {2003e:11046},
  mrreviewer	= {T. C. Vasudevan}
}

@Article{	  fearnley:phd,
  author	= {Fearnley, J.},
  title		= {{V}anishing and {N}on-{V}anishing of {L}-Series of
		  {E}lliptic {C}urves {T}wisted by {D}irichlet {C}haracters},
  year		= 2001,
  journal	= {Concordia Ph.D. thesis}
}

@Article{	  flach:pairing,
  author	= {Flach, M.},
  title		= {A generalisation of the {C}assels-{T}ate pairing},
  journal	= {J. Reine Angew. Math.},
  fjournal	= {Journal f\"ur die Reine und Angewandte Mathematik},
  volume	= {412},
  year		= {1990},
  pages		= {113--127},
  issn		= {0075-4102},
  coden		= {JRMAA8},
  mrclass	= {11G09 (11R23 11S25)},
  mrnumber	= {92b:11037},
  mrreviewer	= {Vincent Fleckinger}
}

@Article{	  fontaine:groupes,
  author	= {Fontaine, J-M.},
  title		= {Groupes finis commutatifs sur les vecteurs de {W}itt},
  journal	= {C. R. Acad. Sci. Paris S\'er. A-B},
  volume	= {280},
  year		= {1975},
  pages		= {Ai, A1423--A1425},
  mrclass	= {14L05},
  mrnumber	= {51 \#10353},
  mrreviewer	= {Robert A. Morris}
}

@InCollection{	  frey-muller,
  author	= {Frey, G. and M{\"u}ller, M.},
  title		= {Arithmetic of modular curves and applications},
  booktitle	= {Algorithmic algebra and number theory (Heidelberg, 1997)},
  pages		= {11--48},
  publisher	= {Springer},
  address	= {Berlin},
  year		= {1999}
}

@InProceedings{	  frey:boston,
  author	= {Frey, G.},
  title		= {On ternary equations of \protect{F}ermat type and
		  relations with elliptic curves},
  booktitle	= {Modular forms and \protect{F}ermat's last theorem (Boston,
		  MA, 1995)},
  pages		= {527--548},
  publisher	= {Springer},
  address	= {New York},
  year		= {1997},
  crossref	= "boston"
}

@Book{		  freyetal,
  title		= {On {A}rtin's conjecture for odd 2-dimensional
		  representations},
  booktitle	= {On {A}rtin's conjecture for odd 2-dimensional
		  representations},
  editor	= {Frey, G.},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1994},
  pages		= {viii+148},
  isbn		= {3-540-58387-4}
}

@Article{	  freyone,
  author	= {Frey, G.},
  title		= {Links between stable elliptic curves and certain
		  {D}iophantine \protect{\nobreak{equations}}},
  journal	= {Ann. Univ. Sarav. Ser. Math.},
  fjournal	= {Annales Universitatis Saraviensis. Series Mathematicae},
  volume	= {1},
  year		= {1986},
  number	= {1},
  pages		= {iv+40}
}

@InCollection{	  freytwo,
  author	= {Frey, G.},
  title		= {Links between solutions of \protect{${A}-{B}={C}$} and
		  elliptic curves},
  booktitle	= {Number theory (Ulm, 1987)},
  pages		= {31--62},
  publisher	= {Springer},
  address	= {New York},
  year		= {1989}
}

@InCollection{	  frohlich:local,
  author	= {Fr{\"o}hlich, A.},
  title		= {Local fields},
  booktitle	= {Algebraic Number Theory (Proc. Instructional Conf.,
		  Brighton, 1965) },
  pages		= {1--41},
  publisher	= {Thompson, Washington, D.C.},
  year		= {1967}
}

@Article{	  fujiwara,
  author	= {Fujiwara, K.},
  title		= {Level optimization in the totally real case},
  journal	= {in preparation},
  year		= {1999}
}

@Article{	  galbraith,
  author	= {Galbraith, S.\thinspace{}D.},
  title		= {Equations for modular curves},
  year		= {1996},
  journal	= {Oxford Ph.D. thesis},
  pages		= {91 pp.}
}

@article {gonz-lario:manin,
    AUTHOR = {Gonz{\'a}lez, Josep and Lario, Joan-C.},
     TITLE = {{$\bold Q$}-curves and their {M}anin ideals},
   JOURNAL = {Amer. J. Math.},
  FJOURNAL = {American Journal of Mathematics},
    VOLUME = {123},
      YEAR = {2001},
    NUMBER = {3},
     PAGES = {475--503},
      ISSN = {0002-9327},
     CODEN = {AJMAAN},
   MRCLASS = {11G05 (11G18)},
  MRNUMBER = {MR1833149 (2002e:11070)},
MRREVIEWER = {Ivica Gusi{\'c}},
}


@Article{	  generatinghecke,
  author	= "Agashe, A. and Stein, W.\thinspace{}A.",
  title		= {Generating the \protect{H}ecke algebra},
  journal	= {preprint},
  year		= {1999}
}

@Article{	  goldfeld:complexity,
  author	= {Goldfeld, D.},
  title		= {On the computational complexity of modular symbols},
  journal	= {Math. Comp.},
  fjournal	= {Mathematics of Computation},
  volume	= {58},
  year		= {1992},
  number	= {198},
  pages		= {807--814},
  issn		= {0025-5718},
  coden		= {MCMPAF},
  mrclass	= {11F67 (11Y35)},
  mrnumber	= {93a:11042},
  mrrevr	= {Glenn Stevens}
}

@Article{	  goldfeld:l1,
  author	= {Goldfeld, D.},
  title		= {Sur les produits partiels eul\'eriens attach\'es aux
		  courbes elliptiques},
  journal	= {C. R. Acad. Sci. Paris S\'er. I Math.},
  fjournal	= {Comptes Rendus des S\'eances de l'Acad\'emie des Sciences.
		  S\'erie I. Math\'ematique},
  volume	= {294},
  year		= {1982},
  number	= {14},
  pages		= {471--474},
  issn		= {0249-6321},
  coden		= {CHASAP},
  mrclass	= {14K15 (12A70 14G10 14K07)},
  mrnumber	= {84d:14031},
  mrreviewer	= {Andrew Bremner}
}

@Article{	  gonzalez-lario:manin,
  author	= {Gonz{\'a}lez, J. and Lario, J.-C.},
  title		= {{$\mathbf{Q}$}-curves and their {M}anin ideals},
  journal	= {Amer. J. Math.},
  fjournal	= {American Journal of Mathematics},
  volume	= {123},
  year		= {2001},
  number	= {3},
  pages		= {475--503},
  issn		= {0002-9327},
  coden		= {AJMAAN},
  mrclass	= {11G05 (11G18)},
  mrnumber	= {2002e:11070},
  mrreviewer	= {Ivica Gusi{\'c}}
}

@Article{	  mcgraw-ono:vis,
    AUTHOR = {McGraw, William J. and Ono, Ken},
     TITLE = {Modular form congruences and {S}elmer groups},
   JOURNAL = {J. London Math. Soc. (2)},
  FJOURNAL = {Journal of the London Mathematical Society. Second Series},
    VOLUME = {67},
      YEAR = {2003},
    NUMBER = {2},
     PAGES = {302--318},
      ISSN = {0024-6107},
     CODEN = {JLMSAK},
   MRCLASS = {11F33 (11F37 11F67 11G40)},
  MRNUMBER = {MR1956137 (2004d:11033)},
MRREVIEWER = {Vinayak Vatsal},
}

@InCollection{	  gouvea-mazur:density,
  author	= {Gouv\^{e}a, F.\thinspace{}Q. and Mazur, B.},
  title		= {On the density of modular representations},
  booktitle	= {Computational perspectives on number theory (Chicago, IL,
		  1995)},
  pages		= {127--142},
  publisher	= {Amer. Math. Soc.},
  address	= {Providence, RI},
  year		= {1998},
  mrclass	= {11F33 (11F80)},
  mrnumber	= {99a:11056},
  mrreviewer	= {Andrea Mori}
}

@Article{	  gouvea-mazur:families,
  author	= {Gouv\^ea, F. and Mazur, B.},
  title		= {Families of modular eigenforms},
  journal	= {Math. Comp.},
  fjournal	= {Mathematics of Computation},
  volume	= {58},
  year		= {1992},
  number	= {198},
  pages		= {793--805},
  issn		= {0025-5718},
  coden		= {MCMPAF},
  mrclass	= {11F33 (11Y35 14G20)},
  mrnumber	= {93d:11049},
  mrrevr	= {Bas Edixhoven}
}

@Article{	  gouvea:ordinary,
  author	= {Gouv\^ea, F.\thinspace{}Q.},
  title		= {On the ordinary {H}ecke algebra},
  journal	= {J. Number Theory},
  fjournal	= {Journal of Number Theory},
  volume	= {41},
  year		= {1992},
  number	= {2},
  pages		= {178--198},
  issn		= {0022-314X},
  coden		= {JNUTA9}
}

@Book{		  gouvea:slnm,
  author	= {Gouv\^{e}a, F.\thinspace{}Q.},
  title		= {Arithmetic of $p$-adic modular forms},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1988},
  pages		= {viii+121},
  isbn		= {3-540-18946-7},
  mrclass	= {11F85 (11F80)},
  mrnumber	= {91e:11056},
  mrreviewer	= {Alexey A. Panchishkin}
}

@Book{		  greenberg-harper,
  author	= {Greenberg, M.\thinspace{}J. and Harper, J.\thinspace{}R.},
  title		= {Algebraic topology},
  note		= {A first course},
  publisher	= {Benjamin/Cummings Publishing Co. Inc. Advanced Book
		  Program},
  address	= {Reading, Mass.},
  year		= {1981},
  pages		= {xi+311 pp. (loose errata)},
  isbn		= {0-8053-3558-7; 0-8053-3557-9},
  mrclass	= {55-01},
  mrnumber	= {83b:55001},
  mrrevr	= {J. P. May}
}

@Article{	  gross-kohnen-zagier,
  author	= {Gross, B. and Kohnen, W. and Zagier, D.},
  title		= {Heegner points and derivatives of ${L}$-series. {I}{I}},
  journal	= {Math. Ann.},
  fjournal	= {Mathematische Annalen},
  volume	= {278},
  year		= {1987},
  number	= {1-4},
  pages		= {497--562},
  issn		= {0025-5831},
  coden		= {MAANA3},
  mrclass	= {11G40 (11F30 11G05 11R29 14G10)},
  mrnumber	= {89i:11069},
  mrrevr	= {Lawrence Washington}
}

@Article{	  gross-zagier,
  author	= {Gross, B. and Zagier, D.},
  title		= {Heegner points and derivatives of \protect{${L}$}-series},
  journal	= {Invent. Math.},
  fjournal	= {Inventiones Mathematicae},
  volume	= {84},
  year		= {1986},
  number	= {2},
  pages		= {225--320},
  issn		= {0020-9910},
  coden		= {INVMBH},
  mrclass	= {11G40 (11F11 11G05 14G10)},
  mrnumber	= {87j:11057},
  mrrevr	= {Loren D. Olson}
}

@InCollection{	  gross:central,
  author	= {Gross, B.\thinspace{}H.},
  title		= {${L}$-functions at the central critical point},
  booktitle	= {Motives (Seattle, WA, 1991)},
  pages		= {527--535},
  publisher	= {Amer. Math. Soc.},
  address	= {Providence, RI},
  year		= {1994},
  mrclass	= {11G40 (14G10)},
  mrnumber	= {95a:11060},
  mrrevr	= {Jan Nekov{\'a}{\v{r}}}
}

@InCollection{	  gross:kolyvagin,
  author	= {Gross, B.\thinspace{}H.},
  title		= {Kolyvagin's work on modular elliptic curves},
  booktitle	= {$L$-functions and arithmetic (Durham, 1989)},
  pages		= {235--256},
  publisher	= {Cambridge Univ. Press},
  address	= {Cambridge},
  year		= {1991}
}

@Article{	  gross:tameness,
  author	= {Gross, B.\thinspace{}H.},
  title		= {A tameness criterion for \protect{G}alois representations
		  associated to modular forms (mod \protect{$p$})},
  journal	= {Duke Math. J.},
  fjournal	= {Duke Mathematical Journal},
  volume	= {61},
  year		= {1990},
  number	= {2},
  pages		= {445--517},
  issn		= {0012-7094},
  coden		= {DUMJAO}
}

@Article{	  gross_kudla,
  author	= {Gross, B.\thinspace{}H. and Kudla, S.\thinspace{}S.},
  title		= {Heights and the central critical values of triple product
		  {$L$}-functions},
  journal	= {Compositio Math.},
  fjournal	= {Compositio Mathematica},
  volume	= {81},
  year		= {1992},
  number	= {2},
  pages		= {143--209},
  issn		= {0010-437X},
  coden		= {CMPMAF},
  mrclass	= {11F66 (11F67 11G40 19F27)},
  mrnumber	= {93g:11047},
  mrreviewer	= {Alexey A. Panchishkin}
}

@InCollection{	  grothendieck:brauer1,
  author	= {Grothendieck, Alexander},
  title		= {Le groupe de {B}rauer. {I}. {A}lg\`ebres d'{A}zumaya et
		  interpr\'etations diverses},
  booktitle	= {Dix Expos\'es sur la Cohomologie des Sch\'emas},
  pages		= {46--66},
  publisher	= {North-Holland},
  address	= {Amsterdam},
  year		= {1968},
  mrclass	= {14.55},
  mrnumber	= {39 #5586a}
}

@InCollection{	  grothendieck:brauer2,
  author	= {Grothendieck, Alexander},
  title		= {Le groupe de {B}rauer. {I}{I}. {T}h\'eorie cohomologique},
  booktitle	= {Dix Expos\'es sur la Cohomologie des Sch\'emas},
  pages		= {67--87},
  publisher	= {North-Holland},
  address	= {Amsterdam},
  year		= {1968},
  mrclass	= {14.55},
  mrnumber	= {39 #5586b}
}

@InCollection{	  grothendieck:brauer3,
  author	= {Grothendieck, Alexander},
  title		= {Le groupe de {B}rauer. {I}{I}{I}. {E}xemples et
		  compl\'ements},
  booktitle	= {Dix Expos\'es sur la Cohomologie des Sch\'emas},
  pages		= {88--188},
  publisher	= {North-Holland},
  address	= {Amsterdam},
  year		= {1968},
  mrclass	= {14.55},
  mrnumber	= {39 #5586c},
  mrrevr	= {J. S. Milne}
}

@Book{		  grothendieck:monodromie,
  author	= {Grothendieck, A.},
  title		= {Groupes de monodromie en g\'eom\'etrie alg\'ebrique.
		  \protect{I}},
  note		= {S\'eminaire de G\'eom\'etrie Alg\'ebrique du Bois-Marie
		  1967--1969 (SGA 7 I), Dirig\'e par A. Grothendieck. Avec la
		  collaboration de M. Raynaud et D. S. Rim, Lecture Notes in
		  Mathematics, Vol. 288},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1972},
  pages		= {viii+523}
}

@InCollection{	  gruenberg,
  author	= {Gruenberg, K.},
  title		= {Profinite groups},
  booktitle	= {Algebraic Number Theory (Proc. Instructional Conf.,
		  Brighton, 1965)},
  pages		= {116--127},
  publisher	= {Thompson, Washington, D.C.},
  year		= {1967}
}

@Article{	  guerzhoy:kummer,
  title		= {Searching for {K}ummer congruences in an infinite slope
		  family},
  author	= {Guerzhoy, P.},
  year		= {2000},
  journal	= {Preprint}
}

@Book{		  guy:unsolved,
  author	= {Guy, R.\thinspace{}K.},
  title		= {Unsolved problems in number theory},
  edition	= {Second},
  note		= {Unsolved Problems in Intuitive Mathematics, I},
  publisher	= {Springer-Verlag},
  address	= {New York},
  year		= {1994},
  pages		= {xvi+285},
  isbn		= {0-387-94289-0},
  mrclass	= {11-01 (00A07 11-02)},
  mrnumber	= {96e:11002},
  mrreviewer	= {B. M. M. de Weger}
}

@Book{		  haberland,
  author	= {Haberland, Klaus},
  title		= {Galois cohomology of algebraic number fields},
  note		= {With two appendices by Helmut Koch and Thomas Zink},
  publisher	= {VEB Deutscher Verlag der Wissenschaften},
  address	= {Berlin},
  year		= {1978},
  pages		= {145},
  mrclass	= {12A60},
  mrnumber	= {81i:12009},
  mrrevr	= {Chih-Han Sah}
}

@Book{		  halmos:naive,
  author	= {Halmos, Paul R.},
  title		= {Naive set theory},
  series	= {The University Series in Undergraduate Mathematics},
  publisher	= {D. Van Nostrand Co., Princeton, N.J.-Toronto-London-New
		  York},
  year		= {1960},
  pages		= {vii+104},
  mrclass	= {04.00},
  mrnumber	= {22 \#5575},
  mrreviewer	= {L. Rieger}
}

@Article{	  hardy_littlewood:conjf,
  author	= {Hardy, G.\thinspace{}H. and Littlewood, J.\thinspace{}E.},
  title		= {Some {P}roblems of `{P}artitio {N}umerorum.' {I}{I}{I}.
		  {O}n the {E}xpression of a {N}umber as a {S}um of
		  {P}rimes.},
  journal	= {Acta. Math.},
  volume	= {44},
  year		= {1922},
  pages		= {1--70}
}

@Book{		  hartshorne,
  author	= {Hartshorne, R.},
  title		= {Algebraic {G}eometry},
  note		= {Graduate Texts in Mathematics, No. 52},
  publisher	= {Springer-Verlag},
  address	= {New York},
  year		= {1977},
  pages		= {xvi+496},
  isbn		= {0-387-90244-9}
}
@Article{	  hatada:eigenvalues79,
  author	= {Hatada, K.},
  title		= {Eigenvalues of {H}ecke operators on \protect{${\rm
		  {S}{L}}(2,\,{\bf {Z}})$}},
  journal	= {Math. Ann.},
  fjournal	= {Mathematische Annalen},
  volume	= {239},
  year		= {1979},
  number	= {1},
  pages		= {75--96},
  issn		= {0025-5831},
  coden		= {MAANA3},
  mrclass	= {10D15},
  mrnumber	= {80b:10037},
  mrreviewer	= {Roy Fuller}
}

@Article{	  hatada:general,
  author	= {Hatada, K.},
  title		= {On classical and {$l$}-adic modular forms of levels
		  {$Nl\sp m$} and {$N$}},
  journal	= {J. Number Theory},
  fjournal	= {Journal of Number Theory},
  volume	= {87},
  year		= {2001},
  number	= {1},
  pages		= {1--14},
  issn		= {0022-314X},
  coden		= {JNUTA9},
  mrclass	= {11F11 (11F80 11F85)},
  mrnumber	= {2002e:11054},
  mrreviewer	= {Luis V. Dieulefait}
}

@Article{	  hatada:rationality,
  author	= {Hatada, K.},
  title		= {Multiplicity one theorem and modular symbols},
  journal	= {J. Math. Soc. Japan},
  fjournal	= {Journal of the Mathematical Society of Japan},
  volume	= {33},
  year		= {1981},
  number	= {3},
  pages		= {445--470},
  issn		= {0025-5645},
  coden		= {NISUBC},
  mrclass	= {10D12 (12A65)},
  mrnumber	= {83d:10030},
  mrrevr	= {Wen Ch'ing Winnie Li}
}

@Book{		  hellegouarch:invitation,
  author	= {Hellegouarch, Y.},
  title		= {Invitation aux math\'ematiques de {F}ermat-{W}iles},
  publisher	= {Masson},
  address	= {Paris},
  year		= {1997},
  pages		= {viii+401},
  isbn		= {2-225-83008-8},
  mrclass	= {11-01 (11D41 11F11 11G05 11G18)},
  mrnumber	= {99e:11001},
  mrrevr	= {Massimo Bertolini}
}

@Article{	  hida:invent86,
  author	= {Hida, H.},
  title		= {Galois representations into \protect{${\rm {G}{L}}\sb
		  2({\bf {Z}}\sb p[[{X}]])$} attached to ordinary cusp forms},
  journal	= {Invent. Math.},
  fjournal	= {Inventiones Mathematicae},
  volume	= {85},
  year		= {1986},
  number	= {3},
  pages		= {545--613},
  issn		= {0020-9910},
  coden		= {INVMBH},
  mrclass	= {11F11 (11F33 11F85 11R23)},
  mrnumber	= {87k:11049},
  mrrevr	= {Ernst-Wilhelm Zink}
}

@Article{	  hida:iwasawa,
  author	= {Hida, H.},
  title		= {Iwasawa modules attached to congruences of cusp forms},
  journal	= {Ann. Sci. \'Ecole Norm. Sup. (4)},
  fjournal	= {Annales Scientifiques de l'\'Ecole Normale Sup\'erieure.
		  Quatri\`eme S\'erie},
  volume	= {19},
  year		= {1986},
  number	= {2},
  pages		= {231--273},
  issn		= {0012-9593},
  coden		= {ASENAH},
  mrclass	= {11F33 (11G18 11R23)},
  mrnumber	= {88i:11023},
  mrrevr	= {Yasutaka Ihara}
}

@Article{	  hida:modularity,
  author	= {Hida, H.},
  title		= {Modularity {P}roblems of {$\Q$}-{M}otives and
		  {B}ase-{C}hange},
  journal	= {Preprint, {\tt http://www.math.ucla.edu/~hida/}},
  year		= {2000}
}

@Article{	  hijikata:trace,
  author	= {Hijikata, H.},
  title		= {Explicit formula of the traces of \protect{H}ecke
		  operators for \protect{$\Gamma_0(N)$}},
  journal	= {J. Math. Soc. Japan},
  number	= {1},
  volume	= {26},
  year		= {1974},
  pages		= {56--82}
}

@Book{		  hindry-silverman:diophantine,
  author	= {Hindry, Marc and Silverman, Joseph H.},
  title		= {Diophantine geometry},
  note		= {An introduction},
  publisher	= {Springer-Verlag},
  address	= {New York},
  year		= {2000},
  pages		= {xiv+558},
  isbn		= {0-387-98975-7; 0-387-98981-1},
  mrclass	= {11Gxx (11-02 11G10 11G30 11G50 14G25)},
  mrnumber	= {2001e:11058},
  mrreviewer	= {Dino J. Lorenzini}
}

@InProceedings{	  hpf,
  author	= {Swinnerton-Dyer, H.\thinspace{}P.\thinspace{}F.},
  title		= {On $\ell$-adic representations and congruences for
		  coefficients of modular forms},
  booktitle	= {Proceedings of the International Summer School, University
		  of Antwerp, RUCA, July 17--August 3, 1972},
  pages		= {1--55. Lecture Notes in Math., Vol. 350},
  publisher	= {Springer},
  address	= {Berlin},
  year		= {1973}
}

@Article{	  igusa:fibre,
  author	= {Igusa, J.},
  title		= {Fibre systems of \protect{J}acobian varieties},
  journal	= {Amer. J. Math.},
  volume	= {78},
  year		= {1956},
  pages		= {171--199}
}

@Book{		  jacquet-langlands,
  author	= {Jacquet, H. and Langlands, R.\thinspace{}P.},
  title		= {Automorphic forms on \protect{${\rm {G}{L}}(2)$}},
  note		= {Lecture Notes in Mathematics, Vol. 114},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1970},
  pages		= {vii+548}
}

@Article{	  jarvis:hilbert,
  author	= {Jarvis, F.},
  title		= {On \protect{G}alois representations associated to
		  \protect{H}ilbert modular forms},
  journal	= {J. Reine Angew. Math.},
  fjournal	= {Journal f\"ur die Reine und Angewandte Mathematik},
  volume	= {491},
  year		= {1997},
  pages		= {199--216},
  issn		= {0075-4102},
  coden		= {JRMAA8}
}

@Article{	  jarvis:level,
  author	= {Jarvis, F.},
  title		= {Level lowering for modular mod \protect{$\ell$}
		  representations over totally real fields\-},
  journal	= {Math. Ann.},
  fjournal	= {Mathematische Annalen},
  volume	= {313},
  year		= {1999},
  number	= {1},
  pages		= {141--160},
  issn		= {0025-5831},
  coden		= {MAANA}
}

@Article{	  jarvis:mazur,
  author	= {Jarvis, F.},
  title		= {Mazur's principle for totally real fields of odd degree},
  journal	= {Compositio Math.},
  fjournal	= {Compositio Mathematica},
  volume	= {116},
  year		= {1999},
  number	= {1},
  pages		= {39--79},
  issn		= {0010-437X},
  coden		= {CMPMAF}
}

@InCollection{	  jochnowitz:conjecture,
  author	= {Jochnowitz, N.},
  title		= {A $p$-adic conjecture about derivatives of ${L}$-series
		  attached to modular forms},
  booktitle	= {$p$-adic monodromy and the {B}irch and {S}winnerton-{D}yer
		  conjecture},
  pages		= {239--263},
  publisher	= {Amer. Math. Soc.},
  address	= {Providence, RI},
  year		= {1994},
  mrclass	= {11F33 (11F67 11F85 11G40)},
  mrnumber	= {95g:11037},
  mrrevr	= {Andrea Mori}
}

@Article{	  jochnowitz:duke,
  author	= {Jochnowitz, N.},
  title		= {The index of the {H}ecke ring, ${T}\sb{k}$, in the ring of
		  integers of \protect{${T}\sb{k}\otimes {\bf {Q}}$}},
  journal	= {Duke Math. J.},
  fjournal	= {Duke Mathematical Journal},
  volume	= {46},
  year		= {1979},
  number	= {4},
  pages		= {861--869},
  issn		= {0012-7094},
  coden		= {DUMJAO},
  mrclass	= {10D12},
  mrnumber	= {80k:10023},
  mrrevr	= {Henri Cohen}
}

@Article{	  jochnowitz:local,
  author	= {Jochnowitz, N.},
  title		= {A study of the local components of the \protect{H}ecke
		  algebra mod \protect{$\ell$}},
  journal	= {Trans. Amer. Math. Soc.},
  fjournal	= {Transactions of the American Mathematical Society},
  volume	= {270},
  year		= {1982},
  number	= {1},
  pages		= {253--267},
  issn		= {0002-9947},
  coden		= {TAMTAM}
}

@Article{	  jones:thesis,
  author	= {Jones, D.\thinspace{}M.},
  title		= {On modular {G}alois representations in characteristic
		  $3$},
  year		= {1998},
  journal	= {U.\thinspace{}C. Berkeley Ph.D. thesis}
}

@Article{	  jordan-livne:epsilon,
  author	= {Jordan, B.\thinspace{}W. and Livn{\'e}, R.},
  title		= {Conjecture ``epsilon'' for weight \protect{$k>2$}},
  journal	= {Bull. Amer. Math. Soc. (N.S.)},
  fjournal	= {American Mathematical Society. Bulletin. New Series},
  volume	= {21},
  year		= {1989},
  number	= {1},
  pages		= {51--56},
  issn		= {0273-0979},
  coden		= {BAMOAD}
}

@Article{	  jordan-livne:sha,
  author	= {Jordan, B.\thinspace{}W. and Livn{\'e}, R.},
  title		= {On {A}tkin-{L}ehner quotients of {S}himura curves},
  journal	= {Bull. London Math. Soc.},
  fjournal	= {The Bulletin of the London Mathematical Society},
  volume	= {31},
  year		= {1999},
  number	= {6},
  pages		= {681--685},
  issn		= {0024-6093},
  coden		= {LMSBBT},
  mrclass	= {11G18 (11G10 14G35)},
  mrnumber	= {2000j:11090},
  mrreviewer	= {Chandrashekhar Khare}
}

@Article{	  joshi,
  author	= {Joshi, K.},
  title		= {Remarks on methods of {F}ontaine and {F}altings},
  journal	= {Internat. Math. Res. Notices},
  fjournal	= {International Mathematics Research Notices},
  volume	= {1999},
  number	= {22},
  pages		= {1199--1209},
  issn		= {1073-7928},
  mrclass	= {11Fxx},
  mrnumber	= {1 731 472}
}

@InProceedings{	  jps,
  author	= {Serre, J-P.},
  title		= {Congruences et formes modulaires [d'apr\`es
		  {H}.\thinspace{}{P}.\thinspace{}{F}.\ {S}winnerton-{D}yer]},
  booktitle	= {S\'eminaire Bourbaki, 24e ann\'ee (1971/1972), Exp. No.
		  416},
  pages		= {319--338. Lecture Notes in Math., Vol. 317},
  publisher	= {Springer},
  address	= {Berlin},
  year		= {1973}
}

@article {kato:secret,
    AUTHOR = {Kato, Kazuya},
     TITLE = {{$p$}-adic {H}odge theory and values of zeta functions of
              modular forms},
      NOTE = {Cohomologies $p$-adiques et applications arithm\'etiques. III},
   JOURNAL = {Ast\'erisque},
  FJOURNAL = {Ast\'erisque},
    NUMBER = {295},
      YEAR = {2004},
     PAGES = {ix, 117--290},
      ISSN = {0303-1179},
   MRCLASS = {11F85 (11F67 11G40 11R33 11S80 14G10 14G35)},
  MRNUMBER = {MR2104361},
}


@Article{	  katz:annals75,
  author	= {Katz, N.\thinspace{}M.},
  title		= {Higher congruences between modular forms},
  journal	= {Ann. of Math. (2)},
  volume	= {101},
  year		= {1975},
  pages		= {332--367},
  mrclass	= {10D05 (14K15)},
  mrnumber	= {54 #5120},
  mrrevr	= {Neal Koblitz}
}

@InProceedings{	  katz:antwerp350,
  author	= {Katz, N.\thinspace{}M.},
  title		= {$p$-adic properties of modular schemes and modular forms},
  booktitle	= {Modular functions of one variable, III (Proc. Internat.
		  Summer School, Univ. Antwerp, Antwerp, 1972)},
  pages		= {69--190. Lecture Notes in Mathematics, Vol. 350},
  publisher	= {Springer},
  address	= {Berlin},
  year		= {1973}
}

@Article{	  katz:torsion,
  author	= {Katz, N.\thinspace{}M.},
  title		= {Galois properties of torsion points on abelian varieties},
  journal	= {Invent. Math.},
  fjournal	= {Inventiones Mathematicae},
  volume	= {62},
  year		= {1981},
  number	= {3},
  pages		= {481--502},
  issn		= {0020-9910},
  coden		= {INVMBH},
  mrclass	= {14K15 (10D35 14G05)},
  mrnumber	= {82d:14025},
  mrreviewer	= {Kenneth A. Ribet}
}

@InProceedings{	  katzbonn,
  author	= {Katz, N.\thinspace{}M.},
  title		= {A result on modular forms in characteristic $p$},
  booktitle	= {Modular functions of one variable, V (Proc. Second
		  Internat. Conf., Univ. Bonn, Bonn, 1976)},
  pages		= {53--61. Lecture Notes in Math., Vol. 601},
  publisher	= {Springer},
  address	= {Berlin},
  year		= {1977}
}

@Book{		  katzmazur,
  author	= {Katz, N.\thinspace{}M. and Mazur, B.},
  title		= {Arithmetic moduli of elliptic curves},
  publisher	= {Princeton University Press},
  address	= {Princeton, N.J.},
  year		= {1985},
  pages		= {xiv+514},
  isbn		= {0-691-08349-5, 0-691-08352-5}
}

@Article{	  khare:manu,
  author	= {Khare, C.},
  title		= {Multiplicities of mod $p$ {G}alois representations},
  journal	= {Manuscripta Math.},
  fjournal	= {Manuscripta Mathematica},
  volume	= {95},
  year		= {1998},
  number	= {2},
  pages		= {181--188},
  issn		= {0025-2611},
  coden		= {MSMHB2},
  mrclass	= {11F80 (11F33 11G18)},
  mrnumber	= {98m:11046},
  mrrevr	= {Ian Kiming}
}

@Article{	  klenke:phd,
  author	= "Klenke, T.",
  title		= {Modular {V}arieties and {V}isibility},
  journal	= {Ph.D. thesis, Harvard University},
  year		= {2001}
}

@Book{		  knapp:elliptic,
  author	= {Knapp, A.\thinspace{}W.},
  title		= {Elliptic curves},
  publisher	= {Princeton University Press},
  address	= {Princeton, NJ},
  year		= {1992},
  pages		= {xvi+427},
  isbn		= {0-691-08559-5}
}

@Book{		  koblitz:cong,
  author	= {Koblitz, N.},
  title		= {Introduction to elliptic curves and modular forms},
  series	= {Graduate Texts in Mathematics},
  volume	= {97},
  publisher	= {Springer-Verlag},
  address	= {New York},
  year		= {1984},
  pages		= {viii+248},
  isbn		= {0-387-96029-5},
  mrclass	= {11G05 (11G40 14G25 14K07)},
  mrnumber	= {86c:11040},
  mrreviewer	= {Leslie Jane Federer}
}

@InProceedings{	  kohel-stein:ants4,
  author	= "Kohel, D.\thinspace{}R. and Stein, W.\thinspace{}A.",
  title		= "Component {G}roups of {Q}uotients of \protect{$J_0(N)$}",
  booktitle	= {Proceedings of the 4th International Symposium (ANTS-IV),
		  Leiden, Netherlands, July 2--7, 2000},
  publisher	= {Springer},
  address	= {Berlin},
  year		= {2000}
}

@Article{	  kohel:computing,
  author	= "Kohel, D.\thinspace{}R.",
  title		= "Computing modular curves via quaternions",
  journal	= "Fourth CANT Conference",
  year		= 1997
}

@Article{	  kohel:hecke,
  author	= "Kohel, D.\thinspace{}R.",
  title		= "Hecke Module Structure of Quaternions",
  journal	= "In K. Miyake, ed., {\em Class Field Theory -- Its
		  Centenary and Prospect}, The Advanced Studies in Pure
		  Mathematics Series, Math Soc. Japan."
}

@Article{	  koike:conjtwist,
  author	= "Koike, M.",
  title		= "On certain abelian varieties obtained from new forms of
		  weight $2$ on \protect{$\Gamma_0(3^4)$ and
		  $\Gamma_0(3^5)$}",
  journal	= {Nogoya Math. J.},
  volume	= {62},
  year		= {1976},
  pages		= {29--39}
}

@Article{	  kolyvagin-logachev:finiteness,
  author	= {Kolyvagin, V.\thinspace{}A. and Logachev, D.\thinspace{}Y.},
  title		= {Finiteness of the \protect{S}hafarevich-\protect{T}ate
		  group and the group of rational points for some modular
		  abelian varieties},
  journal	= {Algebra i Analiz},
  fjournal	= {Algebra i Analiz},
  volume	= {1},
  year		= {1989},
  number	= {5},
  pages		= {171--196},
  issn		= {0234-0852}
}

@Article{	  kolyvagin-logachev:totallyreal,
  author	= "Kolyvagin, V.\thinspace{}A. and Logachev,
		  D.\thinspace{}Y.",
  title		= "Finiteness of \protect{$\Sha$} over totally real fields",
  journal	= {Math. USSR Izvestiya},
  volume	= {39},
  year		= {1992},
  number	= {1},
  pages		= {829--853}
}

@InCollection{	  kolyvagin:euler_systems,
  author	= {Kolyvagin, V.\thinspace{}A.},
  title		= {Euler systems},
  booktitle	= {The Grothendieck Festschrift, Vol.\ II},
  pages		= {435--483},
  publisher	= {Birkh\"auser Boston},
  address	= {Boston, MA},
  year		= {1990},
  mrclass	= {11R34 (11G05 11G40 11R29)},
  mrnumber	= {92g:11109},
  mrreviewer	= {Karl Rubin}
}

@InProceedings{	  kolyvagin:mordellweil,
  author	= {Kolyvagin, V.\thinspace{}A.},
  title		= {On the {M}ordell-{W}eil group and the {S}hafarevich-{T}ate
		  group of modular elliptic curves},
  booktitle	= {Proceedings of the International Congress of
		  Mathematicians, Vol.\ I, II (Kyoto, 1990)},
  pages		= {429--436},
  publisher	= {Math. Soc. Japan},
  address	= {Tokyo},
  year		= {1991},
  mrclass	= {11G40 (11G05 14G10)},
  mrnumber	= {93c:11046},
  mrrevr	= {John Jones}
}

@Article{	  kolyvagin:structure_of_selmer,
  author	= {Kolyvagin, V.\thinspace{}A.},
  title		= {On the structure of {S}elmer groups},
  journal	= {Math. Ann.},
  fjournal	= {Mathematische Annalen},
  volume	= {291},
  year		= {1991},
  number	= {2},
  pages		= {253--259},
  issn		= {0025-5831},
  coden		= {MAANA},
  mrclass	= {11G05 (11G40)},
  mrnumber	= {93e:11073},
  mrreviewer	= {Massimo Bertolini}
}

@InCollection{	  kolyvagin:structureofsha,
  author	= {Kolyvagin, V.\thinspace{}A.},
  title		= {On the structure of {S}hafarevich-{T}ate groups},
  booktitle	= {Algebraic geometry (Chicago, IL, 1989)},
  pages		= {94--121},
  publisher	= {Springer},
  address	= {Berlin},
  year		= {1991}
}

@Article{	  kolyvagin:subclass,
  author	= {Kolyvagin, V. A.},
  title		= {Finiteness of ${E}(\mathbf{Q})$ and ${\Sha}({E},\mathbf{Q})$
		  for a subclass of {W}eil curves},
  journal	= {Izv. Akad. Nauk SSSR Ser. Mat.},
  fjournal	= {Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya},
  volume	= {52},
  year		= {1988},
  number	= {3},
  pages		= {522--540, 670--671},
  issn		= {0373-2436},
  mrclass	= {11G05 (11G40 14G25 14K07)},
  mrnumber	= {89m:11056},
  mrreviewer	= {Reinhard B{\"o}lling}
}

@Article{	  kolyvagin:weil,
  author	= {Kolyvagin, V. A.},
  title		= {The {M}ordell-{W}eil and {S}hafarevich-{T}ate groups for
		  {W}eil elliptic curves},
  journal	= {Izv. Akad. Nauk SSSR Ser. Mat.},
  fjournal	= {Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya},
  volume	= {52},
  year		= {1988},
  number	= {6},
  pages		= {1154--1180, 1327},
  issn		= {0373-2436},
  mrclass	= {11G05 (11D41 11G40 14G25 14K07)},
  mrnumber	= {90f:11035},
  mrreviewer	= {Reinhard B{\"o}lling}
}

@Article{	  kramer:largesha,
  author	= {Kramer, K.},
  title		= {A family of semistable elliptic curves with large
		  {T}ate-{S}hafarevitch groups},
  journal	= {Proc. Amer. Math. Soc.},
  fjournal	= {Proceedings of the American Mathematical Society},
  volume	= {89},
  year		= {1983},
  number	= {3},
  pages		= {379--386},
  issn		= {0002-9939},
  coden		= {PAMYAR},
  mrclass	= {14K07 (11G05 14G25)},
  mrnumber	= {85d:14059},
  mrreviewer	= {Reinhard B{\"o}lling}
}

@Book{		  kubert-lang,
  author	= {Kubert, D.\thinspace{}S. and Lang, S.},
  title		= {Modular units},
  series	= {Grundlehren der Mathematischen Wissenschaften [Fundamental
		  Principles of Mathematical Science]},
  volume	= {244},
  publisher	= {Springer-Verlag},
  address	= {New York},
  year		= {1981},
  pages		= {xiii+358},
  isbn		= {0-387-90517-0},
  mrclass	= {12A45 (10D05 14G25)},
  mrnumber	= {84h:12009},
  mrreviewer	= {Roland Gillard}
}

@Article{	  lang-tate,
  author	= {Lang, S. and Tate, J.},
  title		= {Principal homogeneous spaces over abelian varieties},
  journal	= {Amer. J. Math.},
  volume	= {80},
  year		= {1958},
  pages		= {659--684}
}

@Book{		  lang:algebra,
  author	= {Lang, S.},
  title		= {Algebra},
  edition	= {Third},
  publisher	= {Addison-Wesley Publishing Co., Reading, Mass.},
  year		= {1993},
  pages		= {xv+912},
  isbn		= {0-201-55540-9}
}

@Book{		  lang:ant,
  author	= {Lang, S.},
  title		= {Algebraic number theory},
  edition	= {Second},
  publisher	= {Springer-Verlag},
  address	= {New York},
  year		= {1994},
  pages		= {xiv+357},
  isbn		= {0-387-94225-4}
}

@Article{	  lang:finitefields,
  author	= {Lang, S.},
  title		= {Algebraic groups over finite fields},
  journal	= {Amer. J. Math.},
  volume	= {78},
  year		= {1956},
  pages		= {555--563},
  mrclass	= {14.0X},
  mrnumber	= {19,174a},
  mrreviewer	= {P. Roquette}
}

@Book{		  lang:modular,
  author	= {Lang, S.},
  title		= {Introduction to modular forms},
  note		= {With appendixes by D. Zagier and W. Feit, Corrected
		  reprint of the 1976 original},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1995},
  pages		= {x+261},
  isbn		= {3-540-07833-9}
}

@Book{		  lang:nt3,
  author	= {Lang, S.},
  title		= {Number theory. {I}{I}{I}},
  note		= {Diophantine geometry},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1991},
  pages		= {xiv+296},
  isbn		= {3-540-53004-5},
  mrclass	= {11Gxx (14Gxx)},
  mrnumber	= {93a:11048},
  mrreviewer	= {Joseph H. Silverman}
}

@InProceedings{	  langlands:antwerp2,
  author	= {Langlands, R.\thinspace{}P.},
  title		= {Modular forms and $\ell $-adic representations},
  booktitle	= {Proceedings of the International Summer School, University
		  of Antwerp, RUCA, July 17--August 3, 1972},
  editor	= {Deligne, P. and Kuyk, W.},
  pages		= {361--500. Lecture Notes in Math., Vol. 349},
  publisher	= {Springer},
  address	= {Berlin},
  year		= {1973},
  mrclass	= {12A70 (10D15 14G10 22E50)},
  mrnumber	= {50 #7095},
  mrrevr	= {I. I. Pjateckii-Sapiro}
}

@Book{		  langlands:basechange,
  author	= {Langlands, R.\thinspace{}P.},
  title		= {Base change for \protect{${\rm {G}{L}}(2)$}},
  publisher	= {Princeton University Press},
  address	= {Princeton, N.J.},
  year		= {1980},
  pages		= {vii+237},
  isbn		= {0-691-08263-4; 0-691-08272-3}
}

@Article{	  lenstra-oort:additive,
  author	= {Lenstra, Jr., H. W. and Oort, F.},
  title		= {Abelian varieties having purely additive reduction},
  journal	= {J. Pure Appl. Algebra},
  fjournal	= {Journal of Pure and Applied Algebra},
  volume	= {36},
  year		= {1985},
  number	= {3},
  pages		= {281--298},
  issn		= {0022-4049},
  coden		= {JPAAA2},
  mrclass	= {14K15 (11G10 14G20)},
  mrnumber	= {86e:14020},
  mrreviewer	= {Joseph H. Silverman}
}

@InCollection{	  lenstra-smit:explicit,
  author	= {de Smit, B. and Lenstra, H.\thinspace{}W.,Jr.},
  title		= {Explicit construction of universal deformation rings},
  booktitle	= {Modular forms and \protect{F}ermat's last theorem (Boston,
		  MA, 1995)},
  pages		= {313--326},
  publisher	= {Springer},
  address	= {New York},
  year		= {1997}
}

@Book{		  lenstras:nfs,
  title		= {The development of the number field sieve},
  editor	= {Lenstra, A.\thinspace{}K. and Lenstra, Jr.,
		  H.\thinspace{}W.},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1993},
  pages		= {viii+131},
  isbn		= {3-540-57013-6},
  mrclass	= {11Yxx (11-06 11N35 11N36 11Y05 11Y40)},
  mrnumber	= {96m:11116},
  mrreviewer	= {Samuel S. Wagstaff, Jr.}
}

@Article{	  lichtenbaum:curves,
  author	= {Lichtenbaum, Stephen},
  title		= {Curves over discrete valuation rings},
  journal	= {Amer. J. Math.},
  volume	= {90},
  year		= {1968},
  pages		= {380--405},
  mrclass	= {14.20},
  mrnumber	= {37 \#6284},
  mrreviewer	= {J.-E. Bertin}
}

@Article{	  lichtenbaum:duality,
  author	= {Lichtenbaum, S.},
  title		= {Duality theorems for curves over \protect{$p$}-adic
		  fields},
  journal	= {Invent. Math.},
  volume	= {7},
  year		= {1969},
  pages		= {120--136}
}

@Article{	  lidia,
  title		= {\protect{LiDIA: C++} number theory library},
  author	= {Buchmann, J.}
}

@Article{	  livne:conductors,
  author	= {Livn{\'e}, R.},
  title		= {On the conductors of mod \protect{$\ell$} \protect{G}alois
		  representations coming from modular forms},
  journal	= {J. Number Theory},
  fjournal	= {Journal of Number Theory},
  volume	= {31},
  year		= {1989},
  number	= {2},
  pages		= {133--141},
  issn		= {0022-314X},
  coden		= {JNUTA9}
}

@Proceedings{	  lms254,
  title		= {Galois Representations in Arithmetic Algebraic Geometry},
  booktitle	= {Galois Representations in Arithmetic Algebraic Geometry},
  editor	= {Scholl A.\thinspace{}J. and Taylor R.\thinspace{}L.},
  pages		= {493},
  year		= {1998},
  publisher	= {Cambridge University Press}
}

@Article{	  lorenzini:abvarred,
  author	= {Lorenzini, D.\thinspace{}J.},
  title		= "On the Jacobian of the Modular Curve \protect{$X_0(N)$}",
  journal	= "preprint"
}

@Article{	  lorenzini:compgrp,
  author	= {Lorenzini, D.\thinspace{}J.},
  title		= {On the group of components of a \protect{N}\'eron model},
  journal	= {J. Reine Angew. Math.},
  fjournal	= {Journal f\"ur die Reine und Angewandte Mathematik},
  volume	= {445},
  year		= {1993},
  pages		= {109--160},
  issn		= {0075-4102},
  coden		= {JRMAA8}
}

@Article{	  magma,
  author	= {Bosma, W. and Cannon, J. and Playoust, C.},
  title		= {The {M}agma algebra system. {I}. {T}he user language},
  note		= {Computational algebra and number theory (London, 1993)},
  journal	= {J. Symbolic Comput.},
  fjournal	= {Journal of Symbolic Computation},
  volume	= {24},
  year		= {1997},
  number	= {3--4},
  pages		= {235--265},
  issn		= {0747-7171},
  mrclass	= {68Q40},
  mrnumber	= {1 484 478}
}

@Article{	  manin:cyclo,
  author	= {Manin, J.\thinspace{}I.},
  title		= {Cyclotomic fields and modular curves},
  journal	= {Russian Math. Surveys},
  volume	= {26},
  year		= {1971},
  number	= {6},
  pages		= {7--78}
}

@Article{	  manin:parabolic,
  author	= {Manin, J.\thinspace{}I.},
  title		= {Parabolic points and zeta functions of modular curves},
  journal	= {Izv. Akad. Nauk SSSR Ser. Mat.},
  volume	= {36},
  year		= {1972},
  pages		= {19--66},
  mrclass	= {14G10 (10D15 14H25)},
  mrnumber	= {47 \#3396},
  mrrevr	= {K.-B. Gundlach}
}

@Book{		  matsumura,
  author	= {Matsumura, H.},
  title		= {Commutative ring theory},
  note		= {Translated from the Japanese by M. Reid},
  publisher	= {Cambridge University Press},
  address	= {Cambridge},
  year		= {1986},
  pages		= {xiv+320},
  isbn		= {0-521-25916-9},
  mrclass	= {13-01},
  mrnumber	= {88h:13001},
  mrreviewer	= {W. V. Vasconcelos}
}

@Article{	  mazur-sd,
  author	= {Mazur, B. and Swinnerton-Dyer, P.},
  title		= {Arithmetic of {W}eil curves},
  journal	= {Invent. Math.},
  volume	= {25},
  year		= {1974},
  pages		= {1--61},
  mrclass	= {14G05 (10D05)},
  mrnumber	= {50 #7152},
  mrrevr	= {J. S. Milne}
}

@Article{	  mazur-swinnerton-dyer:arithmetic,
  author	= {Mazur, B. and Swinnerton-Dyer, P.},
  title		= {Arithmetic of {W}eil curves},
  journal	= {Invent. Math.},
  volume	= {25},
  year		= {1974},
  pages		= {1--61},
  mrclass	= {14G05 (10D05)},
  mrnumber	= {50 \#7152},
  mrreviewer	= {J. S. Milne}
}

@Article{	  mazur:arithmetic_values,
  author	= {Mazur, B.},
  title		= {On the arithmetic of special values of ${L}$\ functions},
  journal	= {Invent. Math.},
  fjournal	= {Inventiones Mathematicae},
  volume	= {55},
  year		= {1979},
  number	= {3},
  pages		= {207--240},
  issn		= {0020-9910},
  coden		= {INVMBH},
  mrclass	= {14G10 (10D24 12A70 14G25 14K07)},
  mrnumber	= {82e:14033},
  mrrevr	= {V. V. Shokurov}
}

@Article{	  mazur:arizona,
  author	= "Mazur, B.",
  title		= "Three lectures about the arithmetic of elliptic curves.",
  journal	= "To appear in the proceedings from the Arizona Southwest
		  Geometry Winter School",
  year		= 1998
}

@InCollection{	  mazur:deforming,
  author	= {Mazur, B.},
  title		= {Deforming \protect{G}alois representations},
  booktitle	= {Galois groups over \protect{${\bf Q}$} (Berkeley, CA,
		  1987)},
  pages		= {385--437},
  publisher	= {Springer},
  address	= {New York},
  year		= {1989}
}

@Article{	  mazur:eisenstein,
  author	= {Mazur, B.},
  title		= {Modular curves and the \protect{Eisenstein} ideal},
  journal	= {Inst. Hautes \'Etudes Sci. Publ. Math.},
  fjournal	= {Institut des Hautes \'Etudes Scientifiques. Publications
		  Math\'ematiques},
  number	= {47},
  year		= {1977},
  pages		= {33--186 (1978)},
  issn		= {0073-8301},
  coden		= {PMIHA6}
}

@Article{	  mazur:infinite_fern,
  author	= {Mazur, B.},
  title		= {An ``infinite fern'' in the universal deformation space of
		  {G}alois representations},
  note		= {Journ\'ees Arithm\'etiques (Barcelona, 1995)},
  journal	= {Collect. Math.},
  fjournal	= {Universitat de Barcelona. Collectanea Mathematica},
  volume	= {48},
  year		= {1997},
  number	= {1-2},
  pages		= {155--193},
  issn		= {0010-0757},
  coden		= {COLMBA},
  mrclass	= {11F33 (11F80)},
  mrnumber	= {98g:11053},
  mrreviewer	= {Andrea Mori}
}

@Article{	  mazur:rational,
  author	= {Mazur, B.},
  title		= {Rational isogenies of prime degree (with an appendix by
		  {D}. {G}oldfeld)},
  journal	= {Invent. Math.},
  fjournal	= {Inventiones Mathematicae},
  volume	= {44},
  year		= {1978},
  number	= {2},
  pages		= {129--162},
  issn		= {0020-9910},
  coden		= {INVMBH}
}

@InCollection{	  mazur:symboles,
  author	= {Mazur, B.},
  title		= {Courbes elliptiques et symboles modulaires},
  booktitle	= {S\'eminaire Bourbaki, 24\`eme ann\'ee (1971/1972), Exp.
		  No. 414},
  pages		= {277--294. Lecture Notes in Math., Vol. 317},
  publisher	= {Springer},
  address	= {Berlin},
  year		= {1973},
  mrclass	= {14K15 (14G25 10D15)},
  mrnumber	= {55 \#2930},
  mrrevr	= {Jacques Velu}
}

@Article{	  mazur:tower,
  author	= {Mazur, B.},
  title		= {Rational points of abelian varieties with values in towers
		  of number fields},
  journal	= {Invent. Math.},
  volume	= {18},
  year		= {1972},
  pages		= {183--266}
}

@Article{	  mazur:towers,
  author	= {Mazur, B.},
  title		= {Rational points of abelian varieties with values in towers
		  of number fields},
  journal	= {Invent. Math.},
  volume	= {18},
  year		= {1972},
  pages		= {183--266},
  mrclass	= {14G25 (14K15)},
  mrnumber	= {56 3020},
  mrrevr	= {J.\thinspace{}S. Milne}
}

@Article{	  mazur:visord3,
  author	= {Mazur, B.},
  title		= {Visualizing elements of order three in the
		  {S}hafarevich-{T}ate group},
  note		= {Sir Michael Atiyah: a great mathematician of the twentieth
		  century},
  journal	= {Asian J. Math.},
  fjournal	= {The Asian Journal of Mathematics},
  volume	= {3},
  year		= {1999},
  number	= {1},
  pages		= {221--232},
  issn		= {1093-6106},
  mrclass	= {11G05 (14G05)},
  mrnumber	= {2000g:11048},
  mrreviewer	= {Odile Sauzet}
}

@Article{	  mazur:visthree,
  author	= {Mazur, B.},
  title		= {Visualizing elements of order three in the
		  {S}hafarevich-{T}ate group},
  journal	= {Asian J. Math.},
  fjournal	= {The Asian Journal of Mathematics},
  volume	= {3},
  year		= {1999},
  number	= {1},
  pages		= {221--232},
  issn		= {1093-6106},
  mrclass	= {11G05 (14G05)},
  mrnumber	= {2000g:11048},
  mrreviewer	= {Odile Sauzet}
}

@Article{	  mazurtate:13,
  author	= {Mazur, B. and Tate, J.},
  title		= {Points of order $13$ on elliptic curves},
  journal	= {Invent. Math.},
  volume	= {22},
  year		= {1973/74},
  pages		= {41--49},
  mrclass	= {14G05 (14H40 14K15)},
  mrnumber	= {50 \#327},
  mrreviewer	= {F. Oort}
}

@Article{	  mccallum:duality,
  author	= {McCallum, W.\thinspace{}G.},
  title		= {Duality theorems for {N}\'eron models},
  journal	= {Duke Math. J.},
  fjournal	= {Duke Mathematical Journal},
  volume	= {53},
  year		= {1986},
  number	= {4},
  pages		= {1093--1124},
  issn		= {0012-7094},
  coden		= {DUMJAO},
  mrclass	= {14K15 (11G10 14F20)},
  mrnumber	= {88c:14062},
  mrreviewer	= {Gerd Faltings}
}

@InCollection{	  mccallum:kolyvagin,
  author	= {McCallum, W.\thinspace{}G.},
  title		= {Kolyvagin's work on {S}hafarevich-{T}ate groups},
  booktitle	= {$L$-functions and arithmetic (Durham, 1989)},
  pages		= {295--316},
  publisher	= {Cambridge Univ. Press},
  address	= {Cambridge},
  year		= {1991},
  mrclass	= {11G40 (11G05 14G10)},
  mrnumber	= {92m:11062},
  mrreviewer	= {John Jones}
}

@Article{	  merel-stein,
  author	= {Merel, L. and Stein, W.\thinspace{}A.},
  title		= {The field generated by the points of small prime order on
		  an elliptic curve},
  journal	= {Internat. Math. Res. Notices},
  fjournal	= {International Mathematics Research Notices},
  year		= {2001},
  number	= {20},
  pages		= {1075--1082},
  issn		= {1073-7928},
  mrclass	= {11G05},
  mrnumber	= {1 857 596}
}

@InProceedings{	  merel:1585,
  author	= {Merel, L.},
  title		= {Universal \protect{F}ourier expansions of modular forms},
  booktitle	= {On {A}rtin's conjecture for odd 2-dimensional
		  representations},
  pages		= {59--94},
  publisher	= {Springer},
  year		= {1994}
}

@Article{	  merel:cyclo,
  author	= {Merel, L.},
  title		= {Sur la nature non-cyclotomique des points d'ordre fini des
		  courbes elliptiques},
  note		= {With an appendix by E. Kowalski and P. Michel},
  journal	= {Duke Math. J.},
  fjournal	= {Duke Mathematical Journal},
  volume	= {110},
  year		= {2001},
  number	= {1},
  pages		= {81--119},
  issn		= {0012-7094},
  coden		= {DUMJAO},
  mrclass	= {11G05 (11G40 11L40)},
  mrnumber	= {2002k:11080},
  mrreviewer	= {Matthew H. Baker}
}

@Article{	  merel:intersections,
  author	= {Merel, L.},
  title		= {Intersections sur des courbes modulaires},
  journal	= {Manuscripta Math.},
  fjournal	= {Manuscripta Mathematica},
  volume	= {80},
  year		= {1993},
  number	= {3},
  pages		= {283--289},
  issn		= {0025-2611},
  coden		= {MSMHB2},
  mrclass	= {14G35 (11G18)},
  mrnumber	= {94k:14014},
  mrreviewer	= {Douglas L. Ulmer}
}

@Article{	  merel:weil,
  author	= {Merel, L.},
  title		= {L'accouplement de {W}eil entre le sous-groupe de {S}himura
		  et le sous-groupe cuspidal de ${J}\sb 0(p)$},
  journal	= {J. Reine Angew. Math.},
  fjournal	= {Journal f\"ur die Reine und Angewandte Mathematik},
  volume	= {477},
  year		= {1996},
  pages		= {71--115},
  issn		= {0075-4102},
  coden		= {JRMAA8},
  mrclass	= {11G18 (11F67)},
  mrnumber	= {97f:11045},
  mrrevr	= {Jan Nekov{\'a}{\v{r}}}
}

@Article{	  mestre-oesterle,
  author	= {Mestre, J.-F. and Oesterl{\'e}, J.},
  title		= {Method of graphs (unpublished manuscript)}
}

@Article{	  mestre-oesterle:crelle,
  author	= {Mestre, J.-F. and Oesterl{\'e}, J.},
  title		= {Courbes de {W}eil semi-stables de discriminant une
		  puissance \protect{$m$}-i\`eme},
  journal	= {J. Reine Angew. Math.},
  fjournal	= {Journal f\"ur die Reine und Angewandte Mathematik},
  volume	= {400},
  year		= {1989},
  pages		= {173--184},
  issn		= {0075-4102},
  coden		= {JRMAA8},
  mrclass	= {11G18 (11F70 11G05 14G25 14K07)},
  mrnumber	= {90g:11078},
  mrrevr	= {Noriko Yui}
}

@Article{	  mestre:graphs,
  author	= {Mestre, J.-F.},
  title		= {La m\'ethode des graphes. \protect{Exemples} et
		  applications},
  journal	= {Proceedings of the international conference on class
		  numbers and fundamental units of algebraic number fields
		  (Katata)},
  pages		= {217--242},
  publisher	= {Nagoya Univ.},
  address	= {Nagoya},
  year		= {1986}
}

@Article{	  mfd,
  author	= {Stein, W.},
  title		= {The {M}odular {F}orms {D}atabase\\
{\tt http://wstein.org/Tables}},
  year		= {2004}
}

@Article{	  mfd2,
  author	= {Stein, W.},
  title		= {The {ZOPE} {M}odular {F}orms {D}atabase},
  year		= {2004},
  journal	= {\newline{\tt http://wstein.org/mfd}}
}

@InCollection{	  milne:abvars,
  author	= {Milne, J.\thinspace{}S.},
  title		= {Abelian varieties},
  booktitle	= {Arithmetic geometry (Storrs, Conn., 1984)},
  pages		= {103--150},
  publisher	= {Springer},
  address	= {New York},
  year		= {1986}
}

@Article{	  milne:bsdres,
  author	= {Milne, J.\thinspace{}S.},
  title		= {On the arithmetic of abelian varieties},
  journal	= {Invent. Math.},
  volume	= {17},
  year		= {1972},
  pages		= {177--190},
  mrclass	= {14K15 (14G10 14G25)},
  mrnumber	= {48 \#8512},
  mrreviewer	= {T. Ono}
}

@Book{		  milne:duality,
  author	= {Milne, J.\thinspace{}S.},
  title		= {Arithmetic duality theorems},
  publisher	= {Academic Press Inc.},
  address	= {Boston, Mass.},
  year		= {1986},
  pages		= {x+421},
  isbn		= {0-12-498040-6}
}

@Book{		  milne:etale,
  author	= {Milne, J.\thinspace{}S.},
  title		= {\'{E}tale cohomology},
  publisher	= {Princeton University Press},
  address	= {Princeton, N.J.},
  year		= {1980},
  pages		= {xiii+323},
  isbn		= {0-691-08238-3},
  mrclass	= {14-02 (14F20 18F99)},
  mrnumber	= {81j:14002},
  mrrevr	= {G. Horrocks}
}

@Book{		  miyake,
  author	= {Miyake, T.},
  title		= {Modular forms},
  note		= {Translated from the Japanese by Yoshitaka Maeda},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1989},
  pages		= {x+335},
  isbn		= {3-540-50268-8}
}

@Article{	  momose-ozawa,
  title		= {Rational points of modular curves
		  \protect{$X_{\split}(p)$}},
  author	= {Momose and Ozawa},
  year		= 2002,
  journal	= {Preprint}
}

@Proceedings{	  motives,
  title		= {Motives},
  booktitle	= {Proceedings of the AMS-IMS-SIAM Joint Summer Research
		  Conference held at the University of Washington, Seattle,
		  Washington, July 20--August 2, 1991},
  editor	= {Jannsen, Uwe and Kleiman, Steven and Serre, Jean-Pierre},
  publisher	= {American Mathematical Society},
  address	= {Providence, RI},
  year		= {1994},
  pages		= {xiv+747},
  isbn		= {0-8218-1636-5},
  mrclass	= {11-06 (19-06)},
  mrnumber	= {94i:11003}
}

@Book{		  mr,
  title		= {\protect{S\'{e}m.} Bourbaki no. 355, 1968/69},
  note		= {Lecture Notes in Mathematics, Vol. 179},
  publisher	= {Springer-Verlag},
  address	= {Berlin and New York},
  year		= {1971}
}

@Book{		  mr2000a:11005,
  title		= {Galois representations in arithmetic algebraic geometry},
  editor	= {Scholl, A. J. and Taylor, R. L.},
  note		= {Papers from the London Mathematical Society Symposium held
		  in Durham, July 9--18, 1996},
  publisher	= {Cambridge University Press},
  address	= {Cambridge},
  year		= {1998},
  pages		= {viii+493},
  isbn		= {0-521-64419-4},
  mrclass	= {11-06},
  mrnumber	= {2000a:11005}
}

@Proceedings{	  mr2000c:11002,
  title		= {Automorphic forms, automorphic representations, and
		  arithmetic},
  booktitle	= {Proceedings of the NSF-CBMS Regional Conference in
		  Mathematics on Euler Products and Eisenstein Series held at
		  Texas Christian University, Fort Worth, TX, May 20--24,
		  1996},
  editor	= {Doran, Robert S. and Dou, Ze-Li and Gilbert, George T.},
  publisher	= {American Mathematical Society},
  address	= {Providence, RI},
  year		= {1999},
  pages		= {xii+278},
  isbn		= {0-8218-0659-9},
  mrclass	= {11-06 (11Fxx)},
  mrnumber	= {2000c:11002}
}

@Proceedings{	  mr2000g:11002,
  title		= {Algorithmic number theory},
  booktitle	= {Proceedings of the 3rd International Symposium (ANTS-III)
		  held at Reed College, Portland, OR, June 21--25, 1998},
  editor	= {Buhler, J. P.},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1998},
  pages		= {x+640},
  isbn		= {3-540-64657-4},
  mrclass	= {11-06 (11Yxx)},
  mrnumber	= {2000g:11002}
}

@Proceedings{	  mr2000g:11002,
  title		= {Algorithmic number theory},
  booktitle	= {Proceedings of the 4th International Symposium (ANTS-IV),
		  Leiden, The Netherlands, July 2--7, 2000},
  editor	= {Wieb Bosma},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {2000},
  pages		= {},
  isbn		= {3540676953}
}

@Book{		  mr2000m:11002,
  author	= {Coates, J. and Greenberg, R. and Ribet, K. A. and Rubin,
		  K.},
  title		= {Arithmetic theory of elliptic curves},
  series	= {Lecture Notes in Mathematics},
  volume	= {1716},
  note		= {Lectures from the 3rd C.I.M.E.\ Session held in Cetraro,
		  July 12--19, 1997, Edited by C. Viola},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1999},
  pages		= {viii+234},
  isbn		= {3-540-66546-3},
  mrclass	= {11-06 (11G05)},
  mrnumber	= {2000m:11002}
}

@Book{		  mr2000m:11002,
  author	= {Coates, J. and Greenberg, R. and Ribet, K. A. and Rubin,
		  K.},
  title		= {Arithmetic theory of elliptic curves},
  note		= {Lectures from the 3rd C.I.M.E.\ Session held in Cetraro,
		  July 12--19, 1997, Edited by C. Viola},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1999},
  pages		= {viii+234},
  isbn		= {3-540-66546-3},
  mrclass	= {11-06 (11G05)},
  mrnumber	= {2000m:11002}
}

@Book{		  mr2002d:11003,
  title		= {Arithmetic algebraic geometry},
  series	= {IAS/Park City Mathematics Series},
  volume	= {9},
  editor	= {Conrad, Brian and Rubin, Karl},
  note		= {Including papers from the Graduate Summer School of the
		  Institute for Advanced Study/Park City Mathematics
		  Institute held in Park City, UT, June 20--July 10, 1999},
  publisher	= {American Mathematical Society},
  address	= {Providence, RI},
  year		= {2001},
  pages		= {xiv+569},
  isbn		= {0-8218-2173-3},
  mrclass	= {11-06 (14-06)},
  mrnumber	= {2002d:11003}
}

@Book{		  mr35:6500,
  title		= {Algebraic number theory},
  booktitle	= {Proceedings of an instructional conference organized by
		  the London Mathematical Society (a NATO Advanced Study
		  Institute) with the support of the Inter national
		  Mathematical Union. Edited by J. W. S. Cassels and A.
		  Fr\"ohlich},
  publisher	= {Academic Press},
  address	= {London},
  year		= {1967},
  pages		= {xviii+366}
}

@Book{		  mr37:3885,
  title		= {Proceedings of a {C}onference on {L}ocal {F}ields},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1967},
  pages		= {v+214},
  mrclass	= {00.04 (12.00)},
  mrnumber	= {37 \#3885}
}

@Book{		  mr48:2080,
  title		= {Modular functions of one variable. {I}{I}{I}},
  booktitle	= {Proceedings of the International Summer School, University
		  of Antwerp, RUCA, July 17--August 3, 1972},
  editor	= {Kuyk, Willem and Serre, J.-P.},
  note		= {Lecture Notes in Mathematics, Vol. 350},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1973},
  pages		= {iv+350},
  mrclass	= {10D05 (14K22)},
  mrnumber	= {48 #2080}
}

@Book{		  mr48:2080,
  title		= {Modular functions of one variable. {I}{I}{I}},
  booktitle	= {Proceedings of the International Summer School, University
		  of Antwerp, RUCA, July 17--August 3, 1972},
  editor	= {Kuyk, W. and Serre, J-P.},
  note		= {Lecture Notes in Mathematics, Vol. 350},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1973},
  pages		= {iv+350}
}

@Book{		  mr48:5967,
  title		= {Analytic number theory},
  booktitle	= {Proceedings of Symposia in Pure Mathematics, Vol. XXIV},
  editor	= {Diamond, Harold G.},
  publisher	= {American Mathematical Society},
  address	= {Providence, R.I.},
  year		= {1973},
  pages		= {xii+340},
  mrclass	= {10-06},
  mrnumber	= {48 \#5967}
}

@Book{		  mr48:5967,
  title		= {Analytic number theory},
  booktitle	= {Proceedings of Symposia in Pure Mathematics, Vol. XXIV},
  editor	= {Diamond, Harold G.},
  publisher	= {American Mathematical Society},
  address	= {Providence, R.I.},
  year		= {1973},
  pages		= {xii+340},
  mrclass	= {10-06},
  mrnumber	= {48 \#5967}
}

@Book{		  mr48:8389,
  title		= {Modular functions of one variable. {I}{I}},
  booktitle	= {Proceedings of the International Summer School, University
		  of Antwerp, RUCA, July 17--August 3, 1972},
  editor	= {Deligne, P. and Kuyk, W.},
  note		= {Lecture Notes in Mathematics, Vol. 349},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1973},
  pages		= {iv+598}
}

@Book{		  mr49:6,
  title		= {Prospects in mathematics},
  booktitle	= {Proceedings of a Symposium, Princeton University,
		  Princeton, N. J., 16--18 March 1970},
  note		= {Annals of Mathematics Studies, No. 70},
  publisher	= {Princeton University Press},
  address	= {Princeton, N.J.},
  year		= {1971},
  pages		= {vii+185},
  mrclass	= {00A10},
  mrnumber	= {49 \#6}
}

@Proceedings{	  mr50:16,
  title		= {S\'eminaire Bourbaki},
  booktitle	= {S\'eminaire Bourbaki, 24\`eme ann\'ee (1971/1972), Exp.
		  No. 414},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1973},
  pages		= {iv+361},
  mrclass	= {00A10},
  mrnumber	= {50 #16}
}

@Book{		  mr50:16,
  title		= {S\'eminaire Bourbaki, 24e ann\'ee (1971/1972), Exp. No.
		  416},
  note		= {Vol. 1971/1972, 24e ann\'ee: Expos\'es Nos. 400--417,
		  Lecture Notes in Mathematics, Vol. 317},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1973},
  pages		= {iv+361},
  mrclass	= {00A10},
  mrnumber	= {50 #16}
}

@Book{		  mr50:4458,
  title		= {Seminar on {M}odern {M}ethods in {N}umber {T}heory},
  note		= {Held at the Institute of Statistical Mathematics, Tokyo,
		  August 30--September 4, 1971},
  publisher	= {Institute of Statistical Mathematics},
  address	= {Tokyo},
  year		= {1971},
  pages		= {iii+291 pp. (not consecutively paged)},
  mrclass	= {10-06},
  mrnumber	= {50 #4458}
}

@Book{		  mr52:8007,
  title		= {S\'eminaire de {T}h\'eorie des {N}ombres. 1971--1972},
  note		= {Tenu \`a l'Universit\'e de Bordeaux I, Talence, ann\'ee
		  universitaire 1971--1972},
  publisher	= {Laboratoire de Th\'eorie des Nombres, Centre National de
		  Recherche Scientifique, Talence},
  year		= {1972},
  pages		= {224 pp. (not consecutively paged)}
}

@Book{		  mr56:11675,
  title		= {Number theory and algebra},
  editor	= {Zassenhaus, H.},
  note		= {Collected papers dedicated to Henry B. Mann, Arnold E.
		  Ross, and Olga Taussky-Todd},
  publisher	= {Academic Press [Harcourt Brace Jovanovich Publishers]},
  address	= {New York},
  year		= {1977},
  pages		= {x1vi+393},
  isbn		= {0-12-776350-3.}
}

@Proceedings{	  mr82d:10006,
  title		= {Theory of numbers},
  series	= {Proceedings of Symposia in Pure Mathematics},
  booktitle	= {Proceedings of the Symposium in Pure Mathematics, VIII},
  editor	= {Whiteman, Albert Leon},
  note		= {Corrected reprint of the 1965 original},
  publisher	= {American Mathematical Society},
  address	= {Providence, R.I.},
  year		= {1979},
  pages		= {vii+216},
  isbn		= {0-8218-1408-7},
  mrclass	= {10-06},
  mrnumber	= {82d:10006}
}

@Book{		  mr82j:10004,
  title		= {S\'eminaire de {T}h\'eorie des {N}ombres, {P}aris 1979--80},
  series	= {Progress in Mathematics},
  volume	= {12},
  editor	= {Bertin, Marie-Jos{\'e}},
  note		= {S\'eminaire Delange-Pisot-Poitou. [Delange-Pisot-Poitou
		  Seminar], Held in Paris, 1979--80},
  publisher	= {Birkh\"auser Boston},
  address	= {Mass.},
  year		= {1981},
  pages		= {ix+394},
  isbn		= {3-7643-3035-X},
  mrclass	= {10-06},
  mrnumber	= {82j:10004}
}

@Proceedings{	  mr86e:00018,
  title		= {Arbeitstagung {B}onn 1984},
  booktitle	= {Proceedings of the 25th mathematical workshop held at the
		  Max-Planck-Institut f\"ur Mathematik, Bonn, June 15--22,
		  1984},
  editor	= {Hirzebruch, F. and Schwermer, J. and Suter, S.},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1985},
  pages		= {iii+481},
  isbn		= {3-540-15195-8}
}

@Proceedings{	  mr86g:00010,
  title		= {Proceedings of the international congress of
		  mathematicians. {V}ol. 1, 2},
  editor	= {Ciesielski, Zbigniew and Olech, Czes{\l}aw},
  note		= {Held in Warsaw, August 16--24, 1983},
  publisher	= {PWN---Polish Scientific Publishers},
  address	= {Warsaw},
  year		= {1984},
  pages		= {lxii+1730},
  isbn		= {83-01-05523-5}
}

@Proceedings{	  mr87m:11004,
  title		= {Number theory},
  booktitle	= {Proceedings of the seminar held at the City University of
		  New York, New York, 1984--1985},
  editor	= {Chudnovsky, D.\thinspace{}V. and Chudnovsky,
		  G.\thinspace{}V. and Cohn, H. and Nathanson,
		  M.\thinspace{}B.},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1987},
  pages		= {vi+324},
  isbn		= {3-540-17669-1}
}

@Proceedings{	  mr88c:14001,
  title		= {Current trends in arithmetical algebraic geometry},
  booktitle	= {Proceedings of the AMS-IMS-SIAM joint summer research
		  conference held at Humboldt State University, Arcata,
		  Calif., August 18--24, 1985},
  editor	= {Ribet, Kenneth A.},
  publisher	= {American Mathematical Society},
  address	= {Providence, R.I.},
  year		= {1987},
  pages		= {x+293},
  isbn		= {0-8218-5070-1}
}

@Book{		  mr89b:14029,
  title		= {Arithmetic geometry},
  editor	= {Cornell, G. and Silverman, J.\thinspace{}H.},
  note		= {Papers from the conference held at the University of
		  Connecticut, Storrs, Conn., July 30--August 10, 1984},
  publisher	= {Springer-Verlag},
  address	= {New York},
  year		= {1986},
  pages		= {xvi+353},
  isbn		= {0-387-96311-1}
}

@Book{		  mr89b:14029,
  title		= {Arithmetic geometry},
  editor	= {Cornell, Gary and Silverman, Joseph H.},
  note		= {Papers from the conference held at the University of
		  Connecticut, Storrs, Connecticut, July 30--August 10,
		  1984},
  publisher	= {Springer-Verlag},
  address	= {New York},
  year		= {1986},
  pages		= {xvi+353},
  isbn		= {0-387-96311-1},
  mrclass	= {14Gxx (11D41 11Gxx 14G25 14K15)},
  mrnumber	= {89b:14029},
  mrreviewer	= {H. Gillet}
}

@Proceedings{	  mr90b:11003,
  title		= {Number theory},
  booktitle	= {Proceedings of the Fifteenth Journ\'ees Arithm\'etiques
		  held at the University of Ulm, Ulm, September 14--18, 1987},
  editor	= {Schlickewei, H. P. and Wirsing, E.},
  publisher	= {Springer-Verlag},
  address	= {New York},
  year		= {1989},
  pages		= {vi+266},
  isbn		= {0-387-51397-3}
}

@Proceedings{	  mr90h:14001,
  title		= {Arithmetic of complex manifolds},
  booktitle	= {Proceedings of the conference held at the University of
		  Erlangen, Erlangen, May 27--31, 1988},
  editor	= {Barth, W. P. and Lange, H.},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1989},
  pages		= {vi+171},
  isbn		= {3-540-51729-4}
}

@Book{		  mr90j:11004,
  title		= {S\'eminaire de {T}h\'eorie des {N}ombres, {P}aris 1987--88},
  editor	= {Goldstein, Catherine},
  note		= {Papers from the seminar held in Paris, 1987--88},
  publisher	= {Birkh\"auser Boston Inc.},
  address	= {Boston, MA},
  year		= {1990},
  pages		= {viii+350},
  isbn		= {0-8176-3458-4}
}

@Book{		  mr91h:00035,
  title		= {The \protect{G}rothendieck \protect{F}estschrift.
		  \protect{V}ol. \protect{I}},
  editor	= {Cartier, P. and Illusie, L. and Katz, N.\thinspace{}M. and
		  Laumon, G. and Manin, Yu. and Ribet, K.\thinspace{}A.},
  note		= {A collection of articles written in honor of the 60th
		  birthday of Alexander Grothendieck},
  publisher	= {Birkh\"auser Boston Inc.},
  address	= {Boston, MA},
  year		= {1990},
  pages		= {xx+498},
  isbn		= {0-8176-3427-4}
}

@Proceedings{	  mr91k:11003,
  title		= {$L$-functions and arithmetic},
  booktitle	= {Proceedings of the London Mathematical Society Symposium
		  held at the University of Durham, Durham, June 30--July 11,
		  1989},
  editor	= {Coates, J. and Taylor, M. J.},
  publisher	= {Cambridge University Press},
  address	= {Cambridge},
  year		= {1991},
  pages		= {ix+392},
  isbn		= {0-521-38619-5}
}

@Book{		  mr92b:00051,
  title		= {The {G}rothendieck {F}estschrift. {V}ol. {I}{I}},
  editor	= {Cartier, P. and Illusie, L. and Katz, N. M. and Laumon, G.
		  and Ribet, K. A.},
  note		= {A collection of articles written in honor of the 60th
		  birthday of Alexander Grothendieck},
  publisher	= {Birkh\"auser Boston Inc.},
  address	= {Boston, MA},
  year		= {1990},
  pages		= {viii+563},
  isbn		= {0-8176-3428-2},
  mrclass	= {00B30 (11-06 14-06)},
  mrnumber	= {92b:00051}
}

@Proceedings{	  mr92i:11131,
  title		= {Computational number theory},
  booktitle	= {Proceedings of the colloquium held at Kossuth Lajos
		  University, Debrecen, September 4--9, 1989},
  editor	= {Peth{\H{o}}, Attila and Pohst, Michael E. and Williams,
		  Hugh C. and Zimmer, Horst G{\"u}nter},
  publisher	= {Walter de Gruyter \& Co.},
  address	= {Berlin},
  year		= {1991},
  pages		= {xiv+342},
  isbn		= {3-11-012394-0},
  mrclass	= {11Yxx (11-06)},
  mrnumber	= {92i:11131}
}

@Proceedings{	  mr93d:14004,
  title		= {Algebraic geometry},
  booktitle	= {Proceedings of the US-USSR Symposium held at the
		  University of Chicago, Chicago, Illinois, June 20--July 14,
		  1989},
  editor	= {Bloch, S. and Dolgachev, I. and Fulton, W.},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1991},
  pages		= {viii+300},
  isbn		= {3-540-54456-9}
}

@Proceedings{	  mr93k:00030,
  title		= {Algebra and topology 1992},
  booktitle	= {Proceedings of the Seventh KAIST Mathematics Workshop held
		  in Taej\u on, August 11--14, 1992},
  editor	= {Hahn, S. G. and Suh, D. Y.},
  publisher	= {Korea Advanced Institute of Science and Technology
		  Mathematics Research Center},
  address	= {Taej\u on},
  year		= {1992},
  pages		= {x+271},
  mrclass	= {00B25},
  mrnumber	= {93k:00030}
}

@Book{		  mr94m:11006,
  title		= {$p$-adic monodromy and the {B}irch and {S}winnerton-{D}yer
		  conjecture},
  editor	= {Mazur, Barry and Stevens, Glenn},
  note		= {Papers from the workshop held at Boston University,
		  Boston, Massachusetts, August 12--16, 1991},
  publisher	= {American Mathematical Society},
  address	= {Providence, RI},
  year		= {1994},
  pages		= {xiv+315},
  isbn		= {0-8218-5180-2},
  mrclass	= {11-06 (11G40)},
  mrnumber	= {94m:11006}
}

@Book{		  mr95i:11001,
  title		= {On {A}rtin's conjecture for odd 2-dimensional
		  representations},
  editor	= {Frey, G.},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1994},
  pages		= {viii+148},
  isbn		= {3-540-58387-4},
  mrclass	= {11-06 (11F80)},
  mrnumber	= {95i:11001},
  note		= {1585}
}

@Proceedings{	  mr95j:11119,
  title		= {Algorithmic number theory},
  booktitle	= {Proceedings of the First International Symposium (ANTS-I)
		  held at Cornell University, Ithaca, New York, May 6--9,
		  1994},
  editor	= {Adleman, Leonard M. and Huang, Ming-Deh},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1994},
  pages		= {x+323},
  isbn		= {3-540-58691-1}
}

@Book{		  mr96f:11004,
  title		= {Seminar on {F}ermat's {L}ast {T}heorem},
  editor	= {Murty, V. Kumar},
  note		= {Papers from the seminar held at the Fields Institute for
		  Research in Mathematical Sciences, Toronto, Ontario,
		  1993--1994},
  publisher	= {Published by the American Mathematical Society,
		  Providence, RI},
  year		= {1995},
  pages		= {x+265},
  isbn		= {0-8218-0313-1},
  mrclass	= {11-06 (11D41 11G05 11G18)},
  mrnumber	= {96f:11004}
}

@Proceedings{	  mr98g:11001,
  title		= {Computational perspectives on number theory},
  booktitle	= {Proceedings of the conference in honor of A. O. L. Atkin
		  held at the University of Illinois, Chicago, IL, September
		  1995},
  editor	= {Buell, D. A. and Teitelbaum, J. T.},
  publisher	= {American Mathematical Society},
  address	= {Providence, RI},
  year		= {1998},
  pages		= {x+232},
  isbn		= {0-8218-0880-X},
  mrclass	= {11-01 (00B30 11Yxx)},
  mrnumber	= {98g:11001}
}

@Proceedings{	  mr98g:11001,
  title		= {Computational perspectives on number theory},
  booktitle	= {Proceedings of the conference in honor of A. O. L. Atkin
		  held at the University of Illinois, Chicago, IL, September
		  1995},
  editor	= {Buell, D. A. and Teitelbaum, J. T.},
  publisher	= {American Mathematical Society},
  address	= {Providence, RI},
  year		= {1998},
  pages		= {x+232},
  isbn		= {0-8218-0880-X}
}

@Book{		  mr99f:00041,
  title		= {S\'eminaire {B}ourbaki. {V}ol. 9},
  note		= {Ann\'ees 1964/65-1965/66. [Years 1964/65-1965/66],
		  Expos\'es 277--312, Reprint of the edition published by W.
		  A. Benjamin, New York-Amsterdam, 1966 [MR {\bf 33} \#5420l;
		  MR {\bf 34} \#5605]},
  publisher	= {Soci\'et\'e Math\'ematique de France},
  address	= {Paris},
  year		= {1995},
  pages		= {iv+531},
  isbn		= {2-85629-042-6}
}

@Proceedings{	  mr99m:11004,
  title		= {Topics in number theory},
  series	= {Mathematics and its Applications},
  volume	= {467},
  booktitle	= {Proceedings of the conference held at the Pennsylvania
		  State University, University Park, PA, July 31--August 3,
		  1997},
  editor	= {Ahlgren, Scott D. and Andrews, George E. and Ono, Ken},
  note		= {In honor of B. Gordon and S. Chowla},
  publisher	= {Kluwer Academic Publishers},
  address	= {Dordrecht},
  year		= {1999},
  pages		= {viii+258},
  isbn		= {0-7923-5583-0},
  mrclass	= {11-06},
  mrnumber	= {99m:11004}
}

@Book{		  mumford:abvars,
  author	= {Mumford, D.},
  title		= {Abelian varieties},
  note		= {Tata Institute of Fundamental Research Studies in
		  Mathematics, No. 5 },
  publisher	= {Published for the Tata Institute of Fundamental Research,
		  Bombay},
  year		= {1970},
  pages		= {viii+242}
}

@Book{		  mumford:geometric,
  author	= {Mumford, D. and Fogarty, J. and Kirwan, F.},
  title		= {Geometric invariant theory},
  edition	= {Third},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1994},
  pages		= {xiv+292},
  isbn		= {3-540-56963-4}
}

@article {murty-murty:mean,
    AUTHOR = {Murty, M. Ram and Murty, V. Kumar},
     TITLE = {Mean values of derivatives of modular {$L$}-series},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {133},
      YEAR = {1991},
    NUMBER = {3},
     PAGES = {447--475},
      ISSN = {0003-486X},
     CODEN = {ANMAAH},
   MRCLASS = {11F67 (11G05 11G40)},
  MRNUMBER = {MR1109350 (92e:11050)},
MRREVIEWER = {Daniel Bump},
}
@Book{		  murty-murty,
  author	= {Murty, M.\thinspace{}R. and Murty, V.\thinspace{}K.},
  title		= {Non-vanishing of ${L}$-functions and applications},
  publisher	= {Birkh\"auser Verlag},
  address	= {Basel},
  year		= {1997},
  pages		= {xii+196},
  isbn		= {3-7643-5801-7}
}

@InCollection{	  murty:congruence,
  author	= {Murty, M.\thinspace{}R.},
  title		= {Bounds for congruence primes},
  booktitle	= {Automorphic forms, automorphic representations, and
		  arithmetic (Fort Worth, TX, 1996)},
  pages		= {177--192},
  publisher	= {Amer. Math. Soc.},
  address	= {Providence, RI},
  year		= {1999},
  mrclass	= {11F66 (11G05)},
  mrnumber	= {2000g:11038},
  mrrevr	= {Alexey A. Panchishkin}
}

@Article{	  mwrank,
  author	= {Cremona, J.\thinspace{}E.},
  title		= {{\tt mwrank} (computer software)},
  journal	= {\\{\tt
		  http://www.maths.nott.ac.uk/personal/jec/ftp/progs/}}
}

@Article{	  neron,
  author	= {N{\'e}ron, A.},
  title		= {Mod\`eles minimaux des vari\'et\'es ab\'eliennes sur les
		  corps locaux et globaux},
  journal	= {Inst. Hautes \'Etudes Sci. Publ.Math. No.},
  volume	= {21},
  year		= {1964},
  pages		= {128},
  mrclass	= {14.49 (14.51)},
  mrnumber	= {31 \#3423},
  mrreviewer	= {M. Artin}
}

@Book{		  neronmodels,
  author	= {Bosch, S. and L{\"u}tkebohmert, W. and Raynaud, M.},
  title		= {N\'eron models},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1990},
  pages		= {x+325},
  isbn		= {3-540-50587-3},
  mrclass	= {14K15 (11G10 14L15)},
  mrnumber	= {91i:14034},
  mrrevr	= {J. Milne}
}

@Article{	  neumann1,
  author	= {Neumann, O.},
  title		= {Elliptische {K}urven mit vorgeschriebenem
		  {R}eduktionsverhalten. {I}},
  journal	= {Math. Nachr.},
  volume	= {49},
  year		= {1971},
  pages		= {107--123},
  mrclass	= {14K15 (14G25)},
  mrnumber	= {49 \#2767a},
  mrreviewer	= {J. W. S. Cassels}
}

@Article{	  neumann2,
  author	= {Neumann, O.},
  title		= {Elliptische {K}urven mit vorgeschriebenem
		  {R}eduktionsverhalten. {I}{I}},
  journal	= {Math. Nachr.},
  volume	= {56},
  year		= {1973},
  pages		= {269--280},
  mrclass	= {14K15 (14G25)},
  mrnumber	= {49 \#2767b},
  mrreviewer	= {J. W. S. Cassels}
}

@Article{	  ntl,
  title		= {\protect{NTL: Number} theory library},
  author	= {Shoup, V.}
}

@Article{	  ogg:hyperelliptic,
  author	= {Ogg, Andrew P.},
  title		= {Hyperelliptic modular curves},
  journal	= {Bull. Soc. Math. France},
  volume	= {102},
  year		= {1974},
  pages		= {449--462},
  mrclass	= {14G05 (10D05 14H45)},
  mrnumber	= {51 \#514},
  mrreviewer	= {Kuang-yen Shih}
}

@InCollection{	  ogg:rational13,
  author	= {Ogg, A. P.},
  title		= {Rational points on certain elliptic modular curves},
  booktitle	= {Analytic number theory (Proc. Sympos. Pure Math., Vol
		  XXIV, St. Louis Univ., St. Louis, Mo., 1972)},
  pages		= {221--231},
  publisher	= {Amer. Math. Soc.},
  address	= {Providence, R.I.},
  year		= {1973},
  mrclass	= {14G05 (10D05 14K15)},
  mrnumber	= {49 \#2743},
  mrreviewer	= {J. W. S. Cassels}
}

@InCollection{	  ogg:rationalpoints,
  author	= {Ogg, A. P.},
  title		= {Rational points on certain elliptic modular curves},
  booktitle	= {Analytic number theory (Proc. Sympos. Pure Math., Vol
		  XXIV, St. Louis Univ., St. Louis, Mo., 1972)},
  pages		= {221--231},
  publisher	= {Amer. Math. Soc.},
  address	= {Providence, R.I.},
  year		= {1973},
  mrclass	= {14G05 (10D05 14K15)},
  mrnumber	= {49 \#2743},
  mrreviewer	= {J. W. S. Cassels}
}

@Article{	  ogg:ratpoints_finiteorder,
  author	= {Ogg, A.\thinspace{}P.},
  title		= {Rational points of finite order on elliptic curves},
  journal	= {Invent. Math.},
  volume	= {12},
  year		= {1971},
  pages		= {105--111},
  mrclass	= {10D05},
  mrnumber	= {45 \#178},
  mrreviewer	= {K. Mahler}
}

@InCollection{	  ogg:ratpoints_oncertain,
  author	= {Ogg, A. P.},
  title		= {Rational points on certain elliptic modular curves},
  booktitle	= {Analytic number theory (Proc. Sympos. Pure Math., Vol
		  XXIV, St. Louis Univ., St. Louis, Mo., 1972)},
  pages		= {221--231},
  publisher	= {Amer. Math. Soc.},
  address	= {Providence, R.I.},
  year		= {1973},
  mrclass	= {14G05 (10D05 14K15)},
  mrnumber	= {49 \#2743},
  mrreviewer	= {J. W. S. Cassels}
}

@Article{	  ono-mcgraw,
  title		= {Modular form Congruences and Selmer groups},
  author	= {Ono, K. and McGraw W.},
  year		= {2002},
  journal	= {Preprint}
}

@Article{	  ono:partition,
  author	= {Ono, K. and Guo, L.},
  title		= {The partition function and the arithmetic of certain
		  modular \protect{$L$}-functions},
  journal	= {International Mathematical Research Notes},
  number	= {},
  year		= {1999},
  pages		= {}
}

@Article{	  pentium,
  author	= {Edelman, A.},
  title		= {The mathematics of the {P}entium division bug},
  journal	= {SIAM Rev.},
  fjournal	= {SIAM Review. A Publication of the Society for Industrial
		  and Applied Mathematics},
  volume	= {39},
  year		= {1997},
  number	= {1},
  pages		= {54--67},
  issn		= {0036-1445},
  coden		= {SIREAD},
  mrclass	= {68M07},
  mrnumber	= {98a:68009},
  mrreviewer	= {Behrooz Parhami}
}

@Article{	  pizer:alg,
  author	= {Pizer, A.},
  title		= {An algorithm for computing modular forms on
		  \protect{$\Gamma\sb{0}({N})$}},
  journal	= {J. Algebra},
  fjournal	= {Journal of Algebra},
  volume	= {64},
  year		= {1980},
  number	= {2},
  pages		= {340--390},
  issn		= {0021-8693},
  coden		= {JALGA4}
}

@Article{	  pizer:arithmetic,
  author	= {Pizer, A.},
  title		= {On the arithmetic of quaternion algebras},
  journal	= {Acta Arith.},
  volume	= {31},
  year		= {1976},
  number	= {1},
  pages		= {61--89}
}

@Article{	  pizer:arithmetictwo,
  author	= {Pizer, A.},
  title		= {On the arithmetic of quaternion algebras. \protect{II}},
  journal	= {J. Math. Soc. Japan},
  volume	= {28},
  year		= {1976},
  number	= {4},
  pages		= {676--688}
}

@Article{	  pizer:rep,
  author	= {Pizer, A.},
  title		= {The representability of modular forms by theta series},
  journal	= {J. Math. Soc. Japan},
  volume	= {28},
  year		= {1976},
  number	= {4},
  pages		= {689--698}
}

@Article{	  poonen-schaefer,
  author	= {Poonen, B. and Schaefer, E.\thinspace{}F.},
  title		= {Explicit descent for {J}acobians of cyclic covers of the
		  projective line},
  journal	= {J. Reine Angew. Math.},
  fjournal	= {Journal f\"ur die Reine und Angewandte Mathematik},
  volume	= {488},
  year		= {1997},
  pages		= {141--188},
  issn		= {0075-4102},
  coden		= {JRMAA8},
  mrclass	= {11G30 (11G10 14H30 14H40)},
  mrnumber	= {98k:11087},
  mrreviewer	= {David Grant}
}

@Article{	  poonen-stoll,
  author	= {Poonen, B. and Stoll, M.},
  title		= {The {C}assels-{T}ate pairing on polarized abelian
		  varieties},
  journal	= {Ann. of Math. (2)},
  fjournal	= {Annals of Mathematics. Second Series},
  volume	= {150},
  year		= {1999},
  number	= {3},
  pages		= {1109--1149},
  issn		= {0003-486X},
  coden		= {ANMAAH},
  mrclass	= {11G10 (11G30 14H40 14K15)},
  mrnumber	= {2000m:11048},
  mrreviewer	= {Tam{\'a}s Szamuely}
}

@Article{	  pyle:thesis,
  author	= {Pyle, E.},
  title		= {Abelian varieties over {$\Q$} with large endomorphism
		  algebras and their simple components over {$\Qbar$}},
  journal	= {{\tt http://math.berkeley.edu/~ribet/pyle\_thesis.pdf}}
}

@InProceedings{	  queen,
  author	= {Queen, C.},
  title		= {The existence of \protect{$p$}-adic \protect{A}belian
		  \protect{${L}$}-functions},
  booktitle	= {Number theory and algebra},
  pages		= {263--288},
  publisher	= {Academic Press},
  address	= {New York},
  year		= {1977}
}

@Article{	  rama,
  author	= {Ramakrishna, R.},
  title		= {Lifting {G}alois representations},
  journal	= {preprint}
}

@Article{	  ramakrishna:deform,
  author	= {Ramakrishna, R.},
  title		= {Deforming an even representation},
  journal	= {Invent. Math.},
  fjournal	= {Inventiones Mathematicae},
  volume	= {132},
  year		= {1998},
  number	= {3},
  pages		= {563--580},
  issn		= {0020-9910},
  coden		= {INVMBH},
  mrclass	= {11R32 (11R34)},
  mrnumber	= {99h:11128},
  mrrevr	= {Nigel Boston}
}

@Article{	  ramakrishna:lift2,
  author	= {Ramakrishna, R.},
  title		= {Deforming {G}alois representations and the conjectures of
		  {S}erre and {F}ontaine-{M}azur},
  journal	= {preprint, \protect{\tt ftp://math.cornell.edu/pub/ravi}},
  fjournal	= {},
  volume	= {},
  year		= {2000},
  number	= {},
  pages		= {}
}

@Article{	  ramakrishna:lifting,
  author	= {Ramakrishna, R.},
  title		= {Lifting {G}alois representations},
  journal	= {Invent. Math.},
  fjournal	= {Inventiones Mathematicae},
  volume	= {138},
  year		= {1999},
  number	= {3},
  pages		= {537--562},
  issn		= {0020-9910},
  coden		= {INVMBH},
  mrclass	= {11Fxx},
  mrnumber	= {1 719 819}
}

@Article{	  raynaud,
  author	= {Raynaud},
  title		= {I'm not sure which paper}
}

@Article{	  raynaud:ihes,
  author	= {Raynaud, M.},
  title		= {Sp\'ecialisation du foncteur de {P}icard},
  journal	= {Inst. Hautes \'Etudes Sci. Publ. Math. No.},
  volume	= {38},
  year		= {1970},
  pages		= {27--76},
  mrclass	= {14.55},
  mrnumber	= {44 #227},
  mrrevr	= {R. T. Hoobler}
}

@Article{	  raynaud:pp,
  author	= {Raynaud, Michel},
  title		= {Sch\'emas en groupes de type {$(p,\dots, p)$}},
  journal	= {Bull. Soc. Math. France},
  volume	= {102},
  year		= {1974},
  pages		= {241--280},
  mrclass	= {14L20 (14L25)},
  mrnumber	= {54 \#7488},
  mrreviewer	= {F. Oort}
}

@InCollection{	  ribet-stein:serre,
  author	= {Ribet, K.\thinspace{}A. and Stein, W.\thinspace{}A.},
  title		= {Lectures on {S}erre's conjectures},
  booktitle	= {Arithmetic algebraic geometry (Park City, UT, 1999)},
  series	= {IAS/Park City Math. Ser.},
  volume	= {9},
  pages		= {143--232},
  publisher	= {Amer. Math. Soc.},
  address	= {Providence, RI},
  year		= {2001},
  mrclass	= {11F80 (11F66 11G05)},
  mrnumber	= {2002h:11047},
  mrreviewer	= {Chandrashekhar Khare}
}

@InCollection{	  ribet:abvars,
  author	= {Ribet, K.\thinspace{}A.},
  title		= {Abelian varieties over {${\bf Q}$} and modular forms},
  booktitle	= {Algebra and topology 1992 (Taej\u on)},
  pages		= {53--79},
  publisher	= {Korea Adv. Inst. Sci. Tech.},
  address	= {Taej\u on},
  year		= {1992},
  mrclass	= {11G18 (11F33 14G35 14H52)},
  mrnumber	= {94g:11042},
  mrreviewer	= {Bas Edixhoven}
}

@InCollection{	  ribet:endalg,
  author	= {Ribet, K. A.},
  title		= {Endomorphism algebras of abelian varieties attached to
		  newforms of weight {$2$}},
  booktitle	= {Seminar on Number Theory, Paris 1979--80},
  series	= {Progr. Math.},
  volume	= {12},
  pages		= {263--276},
  publisher	= {Birkh\"auser Boston},
  address	= {Mass.},
  year		= {1981},
  mrclass	= {10D15 (14G13)},
  mrnumber	= {82m:10044},
  mrreviewer	= {Wen Ch'ing Winnie Li}
}

@Article{	  ribet:endo,
  author	= {Ribet, K.\thinspace{}A.},
  title		= {Endomorphisms of semi-stable abelian varieties over number
		  fields},
  journal	= {Ann. Math. (2)},
  volume	= {101},
  year		= {1975},
  pages		= {555--562},
  mrclass	= {14K15 (10D05)},
  mrnumber	= {51 \#8120},
  mrreviewer	= {M. Kuga}
}

@InProceedings{	  ribet:galoisattached,
  author	= {Ribet, K.\thinspace{}A.},
  title		= {Galois representations attached to eigenforms with
		  \protect{N}ebentypus},
  booktitle	= {Modular functions of one variable, V (Proc. Second
		  Internat. Conf., Univ. Bonn, Bonn, 1976)},
  pages		= {17--51. Lecture Notes in Math., Vol. 601},
  publisher	= {Springer},
  address	= {Berlin},
  year		= {1977}
}

@Article{	  ribet:galoissurvey,
  author	= {Ribet, K.\thinspace{}A.},
  title		= {Galois representations and modular forms},
  journal	= {Bull. Amer. Math. Soc. (N.S.)},
  fjournal	= {American Mathematical Society. Bulletin. New Series},
  volume	= {32},
  year		= {1995},
  number	= {4},
  pages		= {375--402},
  issn		= {0273-0979},
  coden		= {BAMOAD}
}

@Article{	  ribet:lowering,
  author	= {Ribet, K.\thinspace{}A.},
  title		= {Lowering the levels of modular representations without
		  multiplicity one},
  journal	= {International Mathematics Research Notices},
  year		= {1991},
  pages		= {15--19}
}

@Article{	  ribet:mestreletter,
  author	= {Ribet, K.\thinspace{}A.},
  title		= {Letter to \protect{M}estre},
  year		= {November, 1987}
}

@Article{	  ribet:modreps,
  author	= {Ribet, K.\thinspace{}A.},
  title		= {On modular representations of \protect{${\rm
		  {G}al}(\overline{\bf{Q}}/{\bf {Q}})$} arising from modular
		  forms},
  journal	= {Invent. Math.},
  fjournal	= {Inventiones Mathematicae},
  volume	= {100},
  year		= {1990},
  number	= {2},
  pages		= {431--476},
  issn		= {0020-9910},
  coden		= {INVMBH}
}

@InCollection{	  ribet:raising,
  author	= {Ribet, K.\thinspace{}A.},
  title		= {Raising the levels of modular representations},
  booktitle	= {S\'eminaire de Th\'eorie des Nombres, Paris 1987--88},
  pages		= {259--271},
  publisher	= {Birkh\"auser Boston},
  address	= {Boston, MA},
  year		= {1990}
}

@InCollection{	  ribet:report,
  author	= {Ribet, K.\thinspace{}A.},
  title		= {Report on mod \protect{$\ell$} representations of
		  \protect{${\rm {G}al}(\overline{\bf{Q}}/{\bf {Q}})$}},
  booktitle	= {Motives (Seattle, WA, 1991)},
  pages		= {639--676},
  publisher	= {Amer. Math. Soc.},
  address	= {Providence, RI},
  year		= {1994}
}

@InCollection{	  ribet:torsion,
  author	= {Ribet, K.\thinspace{}A.},
  title		= {Torsion points on ${J}\sb 0({N})$ and {G}alois
		  representations},
  booktitle	= {Arithmetic theory of elliptic curves (Cetraro, 1997)},
  pages		= {145--166},
  publisher	= {Springer},
  address	= {Berlin},
  year		= {1999},
  mrclass	= {11G18 (11F80)},
  mrnumber	= {2001b:11054},
  mrreviewer	= {Matthew H. Baker}
}

@InCollection{	  ribet:torsionj0,
  author	= {Ribet, K.\thinspace{}A.},
  title		= {Torsion points on {$J\sb 0(N)$} and {G}alois
		  representations},
  booktitle	= {Arithmetic theory of elliptic curves (Cetraro, 1997)},
  series	= {Lecture Notes in Math.},
  volume	= {1716},
  pages		= {145--166},
  publisher	= {Springer},
  address	= {Berlin},
  year		= {1999},
  mrclass	= {11G18 (11F80)},
  mrnumber	= {2001b:11054},
  mrreviewer	= {Matthew H. Baker}
}

@Article{	  ribet:toulouse,
  author	= {Ribet, K.\thinspace{}A.},
  title		= {From the \protect{T}aniyama-\protect{S}himura conjecture
		  to \protect{F}ermat's last theorem},
  journal	= {Ann. Fac. Sci. Toulouse Math. (5)},
  fjournal	= {Toulouse. Facult\'e des Sciences. Annales.
		  Math\'ematiques. S\'erie 5},
  volume	= {11},
  year		= {1990},
  number	= {1},
  pages		= {116--139},
  issn		= {0240-2955}
}

@Article{	  ribet:twistsendoalg,
  author	= {Ribet, K.\thinspace{}A.},
  title		= {Twists of modular forms and endomorphisms of abelian
		  varieties},
  journal	= {Math. Ann.},
  fjournal	= {Mathematische Annalen},
  volume	= {253},
  year		= {1980},
  number	= {1},
  pages		= {43--62},
  issn		= {0025-5831},
  coden		= {MAANA3},
  mrclass	= {10D15 (14G13)},
  mrnumber	= {82e:10043},
  mrreviewer	= {Wen Ch'ing Winnie Li}
}

@Book{		  robert:elliptic,
  author	= {Robert, A.},
  title		= {Elliptic curves},
  note		= {Notes from postgraduate lectures given in Lausanne
		  1971/72, Lecture Notes in Mathematics, Vol. 326},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1973},
  pages		= {viii+264},
  mrclass	= {14K15},
  mrnumber	= {50 #4594},
  mrrevr	= {Kuang-yen Shih}
}

@Article{	  rohrlich:cyclo,
  author	= {Rohrlich, D.\thinspace{}E.},
  title		= {On {$L$}-functions of elliptic curves and cyclotomic
		  towers},
  journal	= {Invent. Math.},
  fjournal	= {Inventiones Mathematicae},
  volume	= {75},
  year		= {1984},
  number	= {3},
  pages		= {409--423},
  issn		= {0020-9910},
  coden		= {INVMBH},
  mrclass	= {11G40 (11R23 14G10)},
  mrnumber	= {86g:11038b},
  mrreviewer	= {Karl Rubin}
}

@InCollection{	  rosen:abvars,
  author	= {Rosen, M.},
  title		= {Abelian varieties over \protect{${\bf {C}}$}},
  booktitle	= {Arithmetic geometry (Storrs, Conn., 1984)},
  pages		= {79--101},
  publisher	= {Springer},
  address	= {New York},
  year		= {1986}
}

@Book{		  rubin:book,
  author	= {Rubin, K.},
  title		= {{E}uler {S}ystems},
  note		= {{A}nnals of {M}athematics {S}tudies {\bf 147},
		  \protect{\tt http://math.Stanford.EDU/\~{ }rubin/weyl.html}},
  publisher	= {Princeton University Press},
  year		= {Spring 2000}
}

@Article{	  rubin:cmsha,
  author	= {Rubin, Karl},
  title		= {Tate-{S}hafarevich groups and ${L}$-functions of elliptic
		  curves with complex multiplication},
  journal	= {Invent. Math.},
  fjournal	= {Inventiones Mathematicae},
  volume	= {89},
  year		= {1987},
  number	= {3},
  pages		= {527--559},
  issn		= {0020-9910},
  coden		= {INVMBH}
}

@InCollection{	  rubin:kato,
  author	= {Rubin, K.},
  title		= {Euler systems and modular elliptic curves},
  booktitle	= {Galois representations in arithmetic algebraic geometry
		  (Durham, 1996)},
  pages		= {351--367},
  publisher	= {Cambridge Univ. Press},
  address	= {Cambridge},
  year		= {1998},
  mrclass	= {11G40 (11G05 11R18 11R23)},
  mrnumber	= {2001a:11106},
  mrreviewer	= {Massimo Bertolini}
}

@InCollection{	  rubin:kolyvagin,
  author	= {Rubin, K.},
  title		= {The work of {K}olyvagin on the arithmetic of elliptic
		  curves},
  booktitle	= {Arithmetic of complex manifolds (Erlangen, 1988)},
  pages		= {128--136},
  publisher	= {Springer},
  address	= {Berlin},
  year		= {1989}
}

@Article{	  rubin:main-conjectures,
  author	= {Rubin, K.},
  title		= {The ``main conjectures'' of {I}wasawa theory for imaginary
		  quadratic fields},
  journal	= {Invent. Math.},
  fjournal	= {Inventiones Mathematicae},
  volume	= {103},
  year		= {1991},
  number	= {1},
  pages		= {25--68},
  issn		= {0020-9910},
  coden		= {INVMBH},
  mrclass	= {11R23 (11G05 11G40)},
  mrnumber	= {92f:11151},
  mrrevr	= {M. A. Kenku}
}

@Article{	  saito,
  author	= {Saito, T.},
  title		= {Modular forms and \protect{$p$}-adic {H}odge theory},
  journal	= {Invent. Math.},
  volume	= {129},
  year		= {1997},
  pages		= {607--620}
}

@Article{	  sbtaylor,
  author	= {Shepherd-Barron, N. I. and Taylor, R.},
  title		= {Mod 2 and mod 5 icosahedral representations},
  journal	= {J. Amer. Math. Soc.},
  fjournal	= {Journal of the American Mathematical Society},
  volume	= {10},
  year		= {1997},
  number	= {2},
  pages		= {283--298},
  issn		= {0894-0347}
}

@Book{		  schilling,
  title		= {Arithmetical algebraic geometry. (\protect{P}roceedings of
		  a \protect{C}onference held at \protect{P}urdue
		  \protect{U}niversity, \protect{D}ecember 5--7, 1963)},
  editor	= {Schilling, O.\thinspace{}F.\thinspace{}G.},
  publisher	= {Harper \& Row Publishers},
  address	= {New York},
  year		= {1965},
  pages		= {vii+200}
}

@Article{	  schneider:iwasawa,
  author	= {Schneider, P.},
  title		= {Iwasawa ${L}$-functions of varieties over algebraic number
		  fields. {A} first approach},
  journal	= {Invent. Math.},
  fjournal	= {Inventiones Mathematicae},
  volume	= {71},
  year		= {1983},
  number	= {2},
  pages		= {251--293},
  issn		= {0020-9910},
  coden		= {INVMBH},
  mrclass	= {11G40 (11G10 14G10 14K15)},
  mrnumber	= {85d:11063},
  mrreviewer	= {Stephen Lichtenbaum}
}

@InCollection{	  scholl:kato,
  author	= {Scholl, A.\thinspace{}J.},
  title		= {An introduction to {K}ato's {E}uler systems},
  booktitle	= {Galois Representations in Arithmetic Algebraic Geometry},
  pages		= {379--460},
  year		= {1998},
  publisher	= {Cambridge University Press}
}

@Article{	  scholl:motivesinvent,
  author	= {Scholl, A.\thinspace{}J.},
  title		= {Motives for modular forms},
  journal	= {Invent. Math.},
  fjournal	= {Inventiones Mathematicae},
  volume	= {100},
  year		= {1990},
  number	= {2},
  pages		= {419--430},
  issn		= {0020-9910},
  coden		= {INVMBH}
}

@Article{	  schur:arith,
  author	= {Schur, I.},
  title		= {Arithmetische {U}ntersuchungen \"uber endliche {G}ruppen
		  linearer {S}ubstitutionen},
  journal	= {Sitz. Pr. Akad. Wiss.},
  year		= {1906},
  pages		= {164--184},
  note		= {Gesam. Abhl., {\bf I}, 177--197, Springer-Verlag,
		  Berlin-Heidelberg-New York-Tokyo, 1973}
}

@InCollection{	  sd:bsd,
  author	= {Swinnerton-Dyer, P.},
  title		= {The conjectures of {B}irch and {S}winnerton-{D}yer, and of
		  {T}ate},
  booktitle	= {Proc. Conf. Local Fields (Driebergen, 1966)},
  pages		= {132--157},
  publisher	= {Springer},
  address	= {Berlin},
  year		= {1967},
  mrclass	= {14.48},
  mrnumber	= {37 \#6287},
  mrreviewer	= {Y. Nakai}
}

@Article{	  serre-tate,
  author	= {Serre, J-P. and Tate, J.\thinspace{}T.},
  title		= {Good reduction of abelian varieties},
  journal	= {Ann. of Math. (2)},
  volume	= {88},
  year		= {1968},
  pages		= {492--517}
}

@Book{		  serre:alggroups,
  author	= {Serre, J-P.},
  title		= {Algebraic groups and class fields},
  note		= {Translated from the French},
  publisher	= {Springer-Verlag},
  address	= {New York},
  year		= {1988},
  pages		= {x+207},
  isbn		= {0-387-96648-X}
}

@InProceedings{	  serre:antwerp72,
  author	= {Serre, J-P.},
  title		= {Formes modulaires et fonctions z\^eta $p$-adiques},
  booktitle	= {Proceedings of the International Summer School, University
		  of Antwerp, RUCA, July 17--August 3, 1972},
  pages		= {191--268. Lecture Notes in Math., Vol. 350},
  publisher	= {Springer},
  address	= {Berlin},
  year		= {1973},
  mrclass	= {10D05},
  mrnumber	= {53 #7949a},
  mrrevr	= {K.-B. Gundlach}
}

@InCollection{	  serre:arcata,
  author	= {Serre, J-P.},
  title		= {Lettre \`a {J}.-{F}. {M}estre},
  booktitle	= {Current trends in arithmetical algebraic geometry (Arcata,
		  Calif., 1985)},
  pages		= {263--268},
  publisher	= {Amer. Math. Soc.},
  address	= {Providence, RI},
  year		= {1987}
}

@Book{		  serre:arithmetic,
  author	= {Serre, J-P.},
  title		= {A \protect{C}ourse in \protect{A}rithmetic},
  note		= {Translated from the French, Graduate Texts in Mathematics,
		  No. 7},
  publisher	= {Springer-Verlag},
  address	= {New York},
  year		= {1973},
  pages		= {viii+115}
}

@InCollection{	  serre:cnrs,
  author	= {Serre, Jean-Pierre},
  title		= {Groupes de {L}ie $l$-adiques attach\'es aux courbes
		  elliptiques},
  booktitle	= {Les Tendances G\'eom. en Alg\'ebre et Th\'eorie des Nombres},
  pages		= {239--256},
  publisher	= {\'Editions du Centre National de la Recherche
		  Scientifique, Paris},
  year		= {1966},
  mrclass	= {14.50},
  mrnumber	= {36 #1453},
  mrrevr	= {H. Popp}
}

@Article{	  serre:conjectures,
  author	= {Serre, J-P.},
  title		= {Sur les repr\'esentations modulaires de degr\'e
		  \protect{$2$} de \protect{${\rm{G}al}(\overline{\bf
		  {Q}}/{\bf {Q}})$}},
  journal	= {Duke Math. J.},
  fjournal	= {Duke Mathematical Journal},
  volume	= {54},
  year		= {1987},
  number	= {1},
  pages		= {179--230},
  issn		= {0012-7094},
  coden		= {DUMJAO}
}

@InCollection{	  serre:discrete,
  author	= {Serre, J-P.},
  title		= {Cohomologie des groupes discrets},
  booktitle	= {Prospects in mathematics (Proc. Sympos., Princeton Univ.,
		  Princeton, N.J., 1970)},
  pages		= {77--169. Ann. of Math. Studies, No. 70},
  publisher	= {Princeton Univ. Press},
  address	= {Princeton, N.J.},
  year		= {1971},
  mrclass	= {22E40 (12A70 20G10 32N99)},
  mrnumber	= {52 \#5876},
  mrreviewer	= {H. Bass}
}

@Article{	  serre:enseign,
  author	= {Serre, J-P.},
  title		= {Divisibilit\'e de certaines fonctions arithm\'etiques},
  journal	= {Enseignement Math. (2)},
  volume	= {22},
  year		= {1976},
  number	= {3-4},
  pages		= {227--260},
  mrclass	= {10H25 (10D05)},
  mrnumber	= {55 #7958},
  mrrevr	= {Larry J. Goldstein}
}

@Book{		  serre:gc,
  author	= {Serre, J-P.},
  title		= {Galois cohomology},
  note		= {Translated from the French by Patrick Ion and revised by
		  the author},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1997},
  pages		= {x+210},
  isbn		= {3-540-61990-9}
}

@Book{		  serre:ladic,
  author	= {Serre, J-P.},
  title		= {Abelian \protect{$\ell$}-adic representations and elliptic
		  curves},
  note		= {With the collaboration of Willem Kuyk and John Labute,
		  Revised reprint of the 1968 original},
  publisher	= {A\thinspace{}K Peters Ltd.},
  address	= {Wellesley, MA},
  year		= {1998},
  pages		= {199},
  isbn		= {1-56881-077-6}
}

@Book{		  serre:lie_theory,
  author	= {Serre, J-P.},
  title		= {Lie algebras and {L}ie groups},
  series	= {Lecture Notes in Mathematics},
  volume	= {1500},
  edition	= {Second},
  note		= {1964 lectures given at Harvard University},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1992},
  pages		= {viii+168},
  isbn		= {3-540-55008-9},
  mrclass	= {17-01 (17Bxx 22-01)},
  mrnumber	= {93h:17001}
}

@Book{		  serre:linear,
  author	= {Serre, J-P.},
  title		= {Linear representations of finite groups},
  note		= {Translated from the second French edition by Leonard L.
		  Scott, Graduate Texts in Mathematics, Vol. 42},
  publisher	= {Springer-Verlag},
  address	= {New York},
  year		= {1977},
  pages		= {x+170},
  isbn		= {0-387-90190-6}
}

@InCollection{	  serre:local,
  author	= {Serre, J-P.},
  title		= {Local class field theory},
  booktitle	= {Algebraic Number Theory (Proc. Instructional Conf.,
		  Brighton, 1965)},
  pages		= {128--161},
  publisher	= {Thompson, Washington, D.C.},
  year		= {1967}
}

@Book{		  serre:localfields,
  author	= {Serre, J-P.},
  title		= {Local fields},
  note		= {Translated from the French by Marvin Jay Greenberg},
  publisher	= {Springer-Verlag},
  address	= {New York},
  year		= {1979},
  pages		= {viii+241},
  isbn		= {0-387-90424-7}
}

@Book{		  serre:oeuvres,
  author	= {Serre, J-P.},
  title		= {{\OE}uvres. {C}ollected papers. {IV}},
  note		= {1985--1998},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {2000},
  pages		= {viii+657},
  isbn		= {3-540-65683-9},
  mrclass	= {01A75 (11-03 12-03 14-03 22E50)},
  mrnumber	= {2001e:01037},
  mrreviewer	= {Alexey A. Panchishkin}
}

@Article{	  serre:propgal,
  author	= {Serre, J-P.},
  title		= {Propri\'et\'es galoisiennes des points d'ordre fini des
		  courbes elliptiques},
  journal	= {Invent. Math.},
  volume	= {15},
  year		= {1972},
  number	= {4},
  pages		= {259--331}
}

@Article{	  serre:propres,
  author	= {Serre, J-P.},
  title		= {Valeurs propres des \protect{op\'{e}rateurs} de
		  \protect{Hecke} modulo \protect{$\ell$}},
  journal	= {\protect{Ast\'{e}risque}},
  volume	= {24--25},
  year		= {1975},
  pages		= {109--117}
}

@Article{	  serre:pseudoreflections,
  author	= {Serre, J-P.},
  title		= {Groupes finis d'automorphismes d'anneaux locaux
		  r\'eguliers},
  journal	= {Colloque d'Alg\`ebre (Paris, 1967), Exp. 8},
  pages		= {11},
  publisher	= {Secr\'etariat math\'ematique},
  address	= {Paris},
  year		= {1968},
  mrclass	= {13.95},
  mrnumber	= {38 \#3267},
  mrreviewer	= {Y. Nakai}
}

@Article{	  serre:travauxwiles,
  author	= {Serre, J-P.},
  title		= {Travaux de {W}iles (et {T}aylor, $\ldots$). {I}},
  note		= {S\'eminaire Bourbaki, Vol.\ 1994/95},
  journal	= {Ast\'erisque},
  fjournal	= {Ast\'erisque},
  number	= {237},
  year		= {1996},
  pages		= {Exp.\ No.\ 803, 5, 319--332},
  issn		= {0303-1179},
  mrclass	= {11G05 (11D41 11F80 11F85 11G18)},
  mrnumber	= {97m:11076},
  mrreviewer	= {Alexey A. Panchishkin}
}

@Article{	  serretau,
  author	= {Serre, J-P.},
  title		= {Une \protect{interpr\'etation} des congruences relatives
		  \protect{\`a} la fonction \protect{$\tau$} de {R}amanujan},
  journal	= {\protect{S\'eminaire Delange-Pisot-Poitou}},
  year		= {1967--68},
  volume	= {\protect{$n^o$} 14}
}

@Article{	  setzer,
  author	= {Setzer, B.},
  title		= {Elliptic curves of prime conductor},
  journal	= {J. London Math. Soc. (2)},
  volume	= {10},
  year		= {1975},
  pages		= {367--378},
  mrclass	= {14K15 (10D05 14G25)},
  mrnumber	= {51 \#8121},
  mrreviewer	= {M. Basmakov}
}

@Book{		  sga3.1,
  author	= {Grothendieck, A.},
  title		= {Sch\'emas en groupes. {I}: {P}ropri\'et\'es g\'en\'erales
		  des sch\'emas en groupes},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1970},
  pages		= {xv+564},
  mrclass	= {14.50},
  mrnumber	= {43 \#223a}
}

@Book{		  sga3.2,
  author	= {Grothendieck, A.},
  title		= {Sch\'emas en groupes. {I}{I}: {G}roupes de type
		  multiplicatif, et structure des sch\'emas en groupes
		  g\'en\'eraux},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1962/1964},
  pages		= {ix+654},
  mrclass	= {14.50},
  mrnumber	= {43 \#223b}
}

@Book{		  sga3.3,
  author	= {Grothendieck, A.},
  title		= {Sch\'emas en groupes. {I}{I}{I}: {S}tructure des sch\'emas
		  en groupes r\'eductifs},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1962/1964},
  pages		= {viii+529},
  mrclass	= {14.50},
  mrnumber	= {43 \#223c}
}

@Book{		  sga7.2,
  author	= {Deligne, P. and Katz, N.},
  title		= {Groupes de monodromie en g\'eom\'etrie alg\'ebrique. {I}{I}},
  note		= {S\'eminaire de G\'eom\'etrie Alg\'ebrique du Bois-Marie
		  1967--1969 (SGA 7 II), Dirig\'e par P. Deligne et N. Katz,
		  Lecture Notes in Mathematics, Vol. 340},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1973},
  pages		= {x+438},
  mrclass	= {14-06},
  mrnumber	= {50 \#7135}
}

@Article{	  shafarevich:exp,
  author	= {Shafarevich, I.\thinspace{}R.},
  title		= {Exponents of elliptic curves},
  journal	= {Dokl. Akad. Nauk SSSR (N.S.)},
  volume	= {114},
  year		= {1957},
  pages		= {714--716}
}

@Article{	  shimizu:zeta,
  author	= {Shimizu, H.},
  title		= {On zeta functions of quaternion algebras},
  journal	= {Ann. of Math. (2)},
  volume	= {81},
  year		= {1965},
  pages		= {166--193}
}

@Article{	  shimura:factors,
  author	= {Shimura, G.},
  title		= {On the factors of the jacobian variety of a modular
		  function field},
  journal	= {J. Math. Soc. Japan},
  volume	= {25},
  number	= {3},
  year		= {1973},
  pages		= {523--544}
}

@Book{		  shimura:intro,
  author	= {Shimura, G.},
  title		= {Introduction to the arithmetic theory of automorphic
		  functions},
  note		= {Reprint of the 1971 original, Kan Memorial Lectures, 1},
  publisher	= {Princeton University Press},
  address	= {Princeton, NJ},
  year		= {1994},
  pages		= {xiv+271},
  isbn		= {0-691-08092-5}
}

@Article{	  shimura:onperiods,
  author	= {Shimura, G.},
  title		= {On the periods of modular forms},
  journal	= {Math. Ann.},
  volume	= {229},
  pages		= {211--221},
  year		= {1977}
}

@Article{	  shimura:reciprocity,
  author	= {Shimura, G.},
  title		= {A reciprocity law in non-solvable extensions},
  journal	= {J. Reine Angew. Math.},
  volume	= {221},
  year		= {1966},
  pages		= {209--220}
}

@Article{	  shimura:surles,
  author	= {Shimura, G.},
  title		= {Sur les \protect{int\'egrales} \protect{attach\'ees} aux
		  formes automorphes},
  journal	= {J. Math. Soc. Japan},
  volume	= {11},
  year		= {1959},
  pages		= {291--311}
}

@Book{		  silverman-tate,
  author	= {Silverman, J.\thinspace{}H. and Tate, J.},
  title		= {Rational points on elliptic curves},
  series	= {Undergraduate Texts in Mathematics},
  publisher	= {Springer-Verlag},
  address	= {New York},
  year		= {1992},
  pages		= {x+281},
  isbn		= {0-387-97825-9},
  mrclass	= {11-01 (11D25 11G05 14H52)},
  mrnumber	= {93g:11003},
  mrreviewer	= {Andrew Bremner}
}

@Book{		  silverman:aec,
  author	= {Silverman, J.\thinspace{}H.},
  title		= {The arithmetic of elliptic curves},
  note		= {Corrected reprint of the 1986 original},
  publisher	= {Springer-Verlag},
  address	= {New York},
  year		= {1992},
  pages		= {xii+400},
  isbn		= {0-387-96203-4}
}

@Book{		  silverman:aec2,
  author	= {Silverman, J.\thinspace{}H.},
  title		= {Advanced topics in the arithmetic of elliptic curves},
  publisher	= {Springer-Verlag},
  address	= {New York},
  year		= {1994},
  pages		= {xiv+525},
  isbn		= {0-387-94328-5}
}

@Article{	  siman_wong:lots_of_sha,
  author	= {Wong, Siman},
  title		= {Elliptic curves and class number divisibility},
  journal	= {Internat. Math. Res. Notices},
  fjournal	= {International Mathematics Research Notices},
  year		= {1999},
  number	= {12},
  pages		= {661--672},
  issn		= {1073-7928},
  mrclass	= {11G05 (11R29)},
  mrnumber	= {2000i:11088},
  mrreviewer	= {Kenneth Kramer}
}

@Article{	  skinner-wiles:ordinary,
  author	= {Skinner, C.\thinspace{}M. and Wiles, A.\thinspace{}J.},
  title		= {Ordinary representations and modular forms},
  journal	= {Proc. Nat. Acad. Sci. U.S.A.},
  fjournal	= {Proceedings of the National Academy of Sciences of the
		  United States of America},
  volume	= {94},
  year		= {1997},
  number	= {20},
  pages		= {10520--10527},
  issn		= {0027-8424},
  coden		= {PNASA6}
}

@Book{		  slnm601,
  title		= {Modular functions of one variable. \protect{V}},
  booktitle	= {Proceedings of the Second International Conference, held
		  at the University of Bonn, Bonn, July 2--14, 1976},
  note		= {Edited by J-P. Serre and D. B. Zagier, Lecture Notes in
		  Mathematics, Vol. 601},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1977},
  pages		= {i+294}
}

@Article{	  sokurov:modsym,
  author	= {{\v{S}}okurov, V. V.},
  title		= {Modular symbols of arbitrary weight},
  journal	= {Funkcional. Anal. i Prilo\v zen.},
  volume	= {10},
  year		= {1976},
  number	= {1},
  pages		= {95--96},
  mrclass	= {10D05},
  mrnumber	= {55 #269},
  mrrevr	= {K.-B. Gundlach}
}

@Article{	  stein-verrill:periods,
  author	= "Stein, W.\thinspace{}A. and Verrill, H.\thinspace{}A.",
  title		= {Computing period lattices associated to newforms},
  journal	= {In preparation},
  year		= {2000}
}

@Article{	  stein-verrill:transportable,
  author	= "Stein, W.\thinspace{}A. and Verrill, H.\thinspace{}A.",
  title		= {Cuspidal modular symbols are transportable},
  journal	= {LMS J. Comput. Math.},
  fjournal	= {LMS Journal of Computation and Mathematics},
  volume	= {4},
  year		= {2001},
  pages		= {170--181 (electronic)},
  issn		= {1461-1570},
  mrclass	= {11F67},
  mrnumber	= {1 901 355}
}

@incollection {stein-watkins:ants5,
    AUTHOR = {Stein, W. and Watkins, M.},
     TITLE = {A database of elliptic curves---first report},
 BOOKTITLE = {Algorithmic number theory (Sydney, 2002)},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {2369},
     PAGES = {267--275},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {2002},
   MRCLASS = {11G05 (11Y35)},
  MRNUMBER = {MR2041090 (2005h:11113)},
   NOTE = {\url{http://wstein.org/ecdb}}
}

@proceedings {MR2041068,
     TITLE = {Algorithmic number theory},
    SERIES = {Lecture Notes in Computer Science},
    VOLUME = {2369},
 BOOKTITLE = {Proceedings of the 5th International Symposium (ANTS-V) held
              at the University of Sydney, Sydney, July 7--12, 2002},
    EDITOR = {Fieker, Claus and Kohel, David R.},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {2002},
     PAGES = {x+517},
      ISBN = {3-540-43863-7},
   MRCLASS = {11-06},
  MRNUMBER = {MR2041068 (2004j:11002)},
}

@Article{	  stein:bsdmagma,
  author	= {Stein, W.},
  title		= {Studying the {B}irch and {S}winnerton-{D}yer {C}onjecture
		  for {M}odular {A}belian {V}arieties {U}sing {MAGMA}},
  journal	= {to appear in J.~Cannon, ed., {\em Computational
		  Experiments in Algebra and Geometry}, Springer-Verlag},
  year		= {2004}
}
@Article{	  stein:congruence,
  author	= "Stein, W.\thinspace{}A.",
  title		= {Congruences between modular forms},
  journal	= {Notes},
  year		= {1999}
}

@Article{	  stein:database,
  author	= "Stein, W.\thinspace{}A.",
  title		= {The modular forms database,\hfill\\ \protect{\tt
		  http://wstein.org}}
}

@Article{	  stein:hecke,
  author	= "Stein, W.\thinspace{}A.",
  title		= {\protect{{\tt HECKE}: The} modular symbols calculator},
  journal	= {Software (available online)},
  year		= {1999}
}

@Article{	  stein:index,
  author	= {Stein, W.\thinspace{}A.},
  title		= {There are genus one curves over {$\mathbf{Q}$} of every
		  odd index},
  journal	= {J. Reine Angew. Math.},
  fjournal	= {Journal f\"ur die Reine und Angewandte Mathematik},
  volume	= {547},
  year		= {2002},
  pages		= {139--147},
  issn		= {0075-4102},
  coden		= {JRMAA8},
  mrclass	= {11G05 (11G18)},
  mrnumber	= {2003c:11059},
  mrreviewer	= {Imin Chen}
}

@Article{	  stein:modsyms,
  author	= "Stein, W.\thinspace{}A.",
  title		= {An introduction to computing modular forms using modular
		  symbols},
  journal	= {to appear in an MSRI Proceedings}
}

@Article{	  stein:nonsquaresha,
  author	= {Stein, W.\thinspace{}A.},
  title		= {Shafarevich-{T}ate {G}roups of {N}onsquare {O}rder},
  publisher	= {Birkh\"auser},
  journal	= {Modular Curves and Abelian Varieties, Progress of
		  Mathematics},
  year		= {2004},
  pages		= {277--289}
}

@Article{	  stein:phd,
  author	= "Stein, W.\thinspace{}A.",
  title		= {Explicit approaches to modular abelian varieties},
  journal	= {Ph.D. thesis, University of California, Berkeley},
  year		= {2000}
}

@Article{	  stein:vismordell,
  author	= {Stein, W.\thinspace{}A.},
  title		= {{V}isualizing {M}ordell-{W}eil {G}roups of {E}lliptic
		  {C}urves {U}sing {S}hafarevich-{T}ate {G}roups},
  year		= {2002},
  journal	= {In preparation}
}

@Article{	  stevens:param,
  author	= {Stevens, G.},
  title		= {Stickelberger elements and modular parametrizations of
		  elliptic curves},
  journal	= {Invent. Math.},
  fjournal	= {Inventiones Mathematicae},
  volume	= {98},
  year		= {1989},
  number	= {1},
  pages		= {75--106},
  issn		= {0020-9910},
  coden		= {INVMBH},
  mrclass	= {11G05 (11F11)},
  mrnumber	= {90m:11089},
  mrreviewer	= {Sheldon Kamienny}
}

@Book{		  stevens:thesis,
  author	= {Stevens, G.},
  title		= {Arithmetic on modular curves},
  publisher	= {Birkh\"auser Boston Inc.},
  address	= {Boston, Mass.},
  year		= {1982},
  pages		= {xvii+214},
  isbn		= {3-7643-3088-0},
  mrclass	= {11G40 (11F67 11G30 14G10 14G13)},
  mrnumber	= {87b:11050},
  mrrevr	= {Ernst Kani}
}

@InCollection{	  sturm:cong,
  author	= {Sturm, J.},
  title		= {On the congruence of modular forms},
  booktitle	= {Number theory (New York, 1984--1985)},
  pages		= {275--280},
  publisher	= {Springer},
  address	= {Berlin},
  year		= {1987}
}

@Book{		  swinnerton-dyer:abvars,
  author	= {Swinnerton-Dyer, H. P. F.},
  title		= {Analytic theory of abelian varieties},
  note		= {London Mathematical Society Lecture Note Series, No. 14},
  publisher	= {Cambridge University Press},
  address	= {London},
  year		= {1974},
  pages		= {viii+90},
  mrclass	= {14K20},
  mrnumber	= {51 \#3180},
  mrreviewer	= {H. Klingen}
}

@InCollection{	  tate:antwerpiv,
  author	= {Tate, J.},
  title		= {Algorithm for determining the type of a singular fiber in
		  an elliptic pencil},
  booktitle	= {Modular functions of one variable, IV (Proc. Internat.
		  Summer School, Univ. Antwerp, Antwerp, 1972)},
  pages		= {33--52. Lecture Notes in Math., Vol. 476},
  publisher	= {Springer},
  address	= {Berlin},
  year		= {1975},
  mrclass	= {14G25 (14K15)},
  mrnumber	= {52 \#13850},
  mrreviewer	= {J. S. Milne}
}

@InCollection{	  tate:bsd,
  author	= {Tate, J.},
  title		= {On the conjectures of {B}irch and {S}winnerton-{D}yer and
		  a geometric analog},
  booktitle	= {S\'eminaire Bourbaki, Vol.\ 9},
  pages		= {Exp.\ No.\ 306, 415--440},
  publisher	= {Soc. Math. France},
  address	= {Paris},
  year		= {1965/66}
}

@InCollection{	  tate:duality,
  author	= {Tate, J.},
  title		= {Duality theorems in {G}alois cohomology over number
		  fields},
  booktitle	= {Proc. Internat. Congr. Mathematicians (Stockholm, 1962)},
  pages		= {288--295},
  publisher	= {Inst. Mittag-Leffler},
  address	= {Djursholm},
  year		= {1963},
  mrclass	= {10.66},
  mrnumber	= {31 \#168}
}

@InCollection{	  tate:global,
  author	= {Tate, J.\thinspace{}T.},
  title		= {Global class field theory},
  booktitle	= {Algebraic Number Theory (Proc. Instructional Conf.,
		  Brighton, 1965)},
  pages		= {162--203},
  publisher	= {Thompson, Washington, D.C.},
  year		= {1967}
}

@Article{	  tate:nonexistence,
  author	= {Tate, J.\thinspace{}T.},
  title		= {The non-existence of certain \protect{Galois} extensions
		  of \protect{$\mathbf{Q}$} unramified outside \protect{$2$}},
  journal	= {Contemporary Math.},
  volume	= {174},
  year		= {1994},
  pages		= {153--156}
}

@Article{	  taylor-wiles:fermat,
  author	= {Taylor, R. and Wiles, A.\thinspace{}J.},
  title		= {Ring-theoretic properties of certain \protect{H}ecke
		  algebras},
  journal	= {Ann. of Math. (2)},
  fjournal	= {Annals of Mathematics. Second Series},
  volume	= {141},
  year		= {1995},
  number	= {3},
  pages		= {553--572},
  issn		= {0003-486X},
  coden		= {ANMAAH}
}

@Article{	  tunnell:artin,
  author	= {Tunnell, J.},
  title		= {Artin's conjecture for representations of octahedral
		  type},
  journal	= {Bull. Amer. Math. Soc. (N.S.)},
  fjournal	= {American Mathematical Society. Bulletin. New Series},
  volume	= {5},
  year		= {1981},
  number	= {2},
  pages		= {173--175},
  issn		= {0002-9904},
  coden		= {BAMOAD}
}

@InProceedings{	  velu:groupes,
  author	= {V\'{e}lu, J.},
  title		= {Groupes de \protect{G}alois attach\'es aux points d'ordre
		  fini des courbes elliptiques sur un corps de nombres,
		  d'apr\`es \protect{J}. \protect{P}. \protect{S}erre},
  booktitle	= {S\'eminaire de Th\'eorie des Nombres, 1971--1972 (Univ.
		  Bordeaux I, Talence), Exp. No. 30},
  pages		= {12},
  publisher	= {Lab. Th\'eorie des Nombres, Centre Nat. Recherche Sci.,
		  Talence},
  year		= {1972}
}

@InProceedings{	  wada1,
  author	= {Wada, H.},
  title		= {Tables of {H}ecke operations. {I}},
  booktitle	= {Seminar on {M}odern {M}ethods in {N}umber {T}heory},
  pages		= {10},
  publisher	= {Inst. Statist. Math.},
  address	= {Tokyo},
  year		= {1971},
  mrclass	= {10D05},
  mrnumber	= {52 #282},
  mrrevr	= {Kuang-yen Shih}
}

@Article{	  waldspurger:comp1,
  author	= {Waldspurger, J.-L.},
  title		= {Quelques propri\'et\'es arithm\'etiques de certaines
		  formes automorphes sur \protect{${\rm {G}{L}}(2)$}},
  journal	= {Compositio Math.},
  fjournal	= {Compositio Mathematica},
  volume	= {54},
  year		= {1985},
  number	= {2},
  pages		= {121--171},
  issn		= {0010-437X},
  coden		= {CMPMAF},
  mrclass	= {11F70 (22E55)},
  mrnumber	= {87g:11061a},
  mrrevr	= {Stephen Gelbart}
}

@Article{	  waldspurger:comp2,
  author	= {Waldspurger, J.-L.},
  title		= {Sur les valeurs de certaines fonctions \protect{${L}$}
		  automorphes en leur centre de sym\'etrie},
  journal	= {Compositio Math.},
  fjournal	= {Compositio Mathematica},
  volume	= {54},
  year		= {1985},
  number	= {2},
  pages		= {173--242},
  issn		= {0010-437X},
  coden		= {CMPMAF},
  mrclass	= {11F70 (11F67 22E55)},
  mrnumber	= {87g:11061b},
  mrrevr	= {Stephen Gelbart}
}

@InProceedings{	  waldspurger:corr,
  author	= {Waldspurger, J.-L.},
  title		= {Correspondances de {S}himura},
  booktitle	= {Proceedings of the International Congress of
		  Mathematicians, Vol.\ 1, 2 (Warsaw, 1983)},
  pages		= {525--531},
  publisher	= {PWN},
  address	= {Warsaw},
  year		= {1984}
}

@Article{	  watanabe:reflections,
  author	= {Watanabe, J.},
  title		= {Some remarks on {C}ohen-{M}acaulay rings with many zero
		  divisors and an application},
  journal	= {J. Algebra},
  volume	= {39},
  year		= {1976},
  number	= {1},
  pages		= {1--14},
  mrclass	= {14M15 (13H10)},
  mrnumber	= {53 \#2968},
  mrreviewer	= {Jean-Luc Chabert}
}

@Article{	  watkins:rankheuristics,
  author	= {Watkins, M.},
  title		= {Some heuristics about elliptic curves},
  journal       = {Preprint},
  year       = {2005}
}


@Article{	  watkins:moddeg,
  author	= {Watkins, M.},
  title		= {Computing the modular degree of an elliptic curve},
  journal	= {Experiment. Math.},
  fjournal	= {Experimental Mathematics},
  volume	= {11},
  year		= {2002},
  number	= {4},
  pages		= {487--502 (2003)},
  issn		= {1058-6458},
  mrclass	= {11G05 (11G18)},
  mrnumber	= {1 969 641}
}

@Article{	  wiles:cmi,
  author	= {Wiles, A.\thinspace{}J.},
  title		= {The {B}irch and {S}winnerton-{D}yer {C}onjecture},
  note		= {\\\protect{\tt
		  http://www.claymath.org/prize\_problems/birchsd.htm}},
  year		= {2000}
}

@Article{	  wiles:fermat,
  author	= {Wiles, A.\thinspace{}J.},
  title		= {Modular elliptic curves and \protect{F}ermat's last
		  theorem},
  journal	= {Ann. of Math. (2)},
  fjournal	= {Annals of Mathematics. Second Series},
  volume	= {141},
  year		= {1995},
  number	= {3},
  pages		= {443--551},
  issn		= {0003-486X},
  coden		= {ANMAAH}
}

@Article{	  winnie:newforms,
  author	= {Li, W-C.},
  title		= {Newforms and functional equations},
  journal	= {Math. Ann.},
  volume	= {212},
  year		= {1975},
  pages		= {285--315}
}

@Article{	  womack:ranktable,
  author	= {Womack, T.},
  title		= {Best known conductors for elliptic curves of given
		  rank,\hfill\\ {\tt
		  http://www.tom.womack.net/maths/conductors.htm}}
}

@InCollection{	  zagier:modular,
  author	= {Zagier, D.},
  title		= {Modular points, modular curves, modular surfaces and
		  modular forms},
  booktitle	= {Workshop Bonn 1984 (Bonn, 1984)},
  pages		= {225--248},
  publisher	= {Springer},
  address	= {Berlin},
  year		= {1985}
}

@Article{	  zagier:parametrizations,
  author	= {Zagier, D.},
  title		= {Modular parametrizations of elliptic curves},
  journal	= {Canad. Math. Bull.},
  fjournal	= {Canadian Mathematical Bulletin},
  volume	= {28},
  year		= {1985},
  number	= {3},
  pages		= {372--384},
  issn		= {0008-4395},
  coden		= {CMBUA3},
  mrclass	= {11G05 (11F11 14G25 14K07 14K15)},
  mrnumber	= {86m:11041},
  mrrevr	= {C.-G. Schmidt}
}

@Book{		  sd:brief,
  author	= {Swinnerton-Dyer, H.\thinspace{}P.\thinspace{}F.},
  title		= {A brief guide to algebraic number theory},
  series	= {London Mathematical Society Student Texts},
  volume	= {50},
  publisher	= {Cambridge University Press},
  address	= {Cambridge},
  year		= {2001},
  pages		= {x+146},
  isbn		= {0-521-00423-3},
  mrclass	= {11Rxx (11-01)},
  mrnumber	= {2002a:11117},
  mrreviewer	= {W. Narkiewicz}
}


@Book{		  weil:adeles,
  author	= {Weil, A.},
  title		= {Adeles and algebraic groups},
  series	= {Progress in Mathematics},
  volume	= {23},
  note		= {With appendices by M. Demazure and Takashi Ono},
  publisher	= {Birkh\"auser Boston},
  address	= {Mass.},
  year		= {1982},
  pages		= {iii+126},
  isbn		= {3-7643-3092-9},
  mrclass	= {10C30 (12A82 12A85 20G35)},
  mrnumber	= {83m:10032},
  mrreviewer	= {K. F. Lai}
}



@book {VignerasAAQ,
    AUTHOR = {Vign{\'e}ras, Marie-France},
     TITLE = {Arithm\'etique des alg\`ebres de quaternions},
    SERIES = {Lecture Notes in Mathematics},
    VOLUME = {800},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {1980},
     PAGES = {vii+169},
      ISBN = {3-540-09983-2},
   MRCLASS = {12A80 (16A18)},
  MRNUMBER = {MR580949 (82i:12016)},
MRREVIEWER = {J. H. H. Chalk},
}

@book {AlsinaBayer,
    AUTHOR = {Alsina, Montserrat and Bayer, Pilar},
     TITLE = {Quaternion orders, quadratic forms, and {S}himura curves},
    SERIES = {CRM Monograph Series},
    VOLUME = {22},
 PUBLISHER = {American Mathematical Society},
   ADDRESS = {Providence, RI},
      YEAR = {2004},
     PAGES = {xvi+196},
      ISBN = {0-8218-3359-6},
   MRCLASS = {11R52 (11G18 11S45)},
  MRNUMBER = {MR2038122 (2005k:11226)},
MRREVIEWER = {Benjamin V. Howard},
}
